How do the requirements to maintain a grapple contrast against the requirements for initiating a grapple? For example, if a paladin successfully initiates a grapple against an orc (using one free hand, per the rules), and the paladin subsequently uses both hands to grasp his greatsword to attack, does the orc cease to be Grappled?
In terms of storytelling, this could go either way; either the paladin must keep one hand on the orc, or the paladin is allowed to maintain an already-established grapple by (for example) hooking an arm or leg onto the orc.
The Rules
The rules require a free hand to start a grapple. The mental image is that the orc can't walk away because the paladin used his hand to grab the orc. This can be intuitively extrapolated into the paladin maintaining the grapple with his hand, but the rules don't explicitly say that this is what happens.
I added bold italics to the bits I found most important.
Grappling
When you want to grab a creature or wrestle with it, you can use the
Attack action to make a special melee attack, a grapple. If you're
able to make multiple attacks with the Attack action, this attack
replaces one of them.The target of your grapple must be no more than one size larger than
you, and it must be within your reach. Using at least one free
hand, you try to seize the target by making a grapple check, a
Strength (Athletics) check contested by the target's Strength
(Athletics) or Dexterity (Acrobatics) check (the target chooses the
ability to use). If you succeed, you subject the target to the
grappled condition (see appendix A). The condition specifies the
things that end it, and you can release the target whenever you
like (no action required).Escaping a Grapple.
A grappled creature can use its action to escape. To do so, it must
succeed on a Strength (Athletics) or Dexterity (Acrobatics) check
contested by your Strength (Athletics) check.Moving a Grappled Creature.
When you move, you can drag or carry the grappled creature with you,
but your speed is halved, unless the creature is two or more sizes
smaller than you. (PHB p.195)
The way I see it, there are two distinct concepts: there's The Grappling procedure, and there's the Grappled condition.
The first half of this text is describing the Grappling procedure. For example, this procedure has certain requirements (including a free hand).
Then comes the sentence, "If you succeed, you subject the target to the grappled condition." This is the connection between the Grappling procedure and the Grappled condition. The Grappling procedure is how you apply the Grappled condition to a target.
The text that comes after "you subject the target to the grappled condition" is about the Grappled condition. I don't believe the earlier text (about the grappling procedure) applies here– but even if I'm right, the text could have been written more clearly, perhaps by explicitly defining the difference between "Grappling" and "Grappled".
In case anyone was hoping the "Grappled condition" rules would help clear this up, here's from Appendix A: Conditions.
A condition lasts either until it is countered (the prone condition is
countered by standing up, for example) or for a duration specified by
the effect that imposed the condition (PHB p.290).
Note that, in the example given, the Prone condition is distinct from whatever event caused the Prone condition.
GRAPPLED
- A grappled creature's speed becomes 0,and it can't benefit from any bonus to its speed.
- The condition ends if the grappler is incapacitated (see the condition).
- The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a
creature is hurled away by the thunderwave spell.
(PHB p.290)
There's no mention of the grappler losing all free hands, shrinking, or otherwise failing to satisfy grappling's initial requirements. There is a mention of an incapacitated grappler automatically ending a grapple, but "Incapacitated" is a much more severe status than not having use of a free hand. I have some thoughts on what this means when I read between the lines– but these are game mechanics; if I'm reading between the lines to be able to obey them, I'm probably not providing a true RAW interpretation.
Going back to the paladin grappling an orc at the beginning, my best guess is that he can use his two-handed weapon without any problem, even though it means he can't start a new grapple until he releases the weapon with one hand. He can also be polymorphed into a mouse and maintain the grapple, even though he won't be able to initiate a new grapple due to size restrictions.
Best Answer
You must release the target to attack, probably ending the grapple
D&D 5e has a broad intent that any word which is not explicitly given special rules meaning, instead has its plain English meaning, though I don't have a citation prepared for it. In plain English we see this:
While "release" technically has multiple meanings, I find this context unambiguous in having Release mean "stop holding with your hand". From this plain English reading, I think it's clear that between the time that you "seize the target" and the time that you "release the target" your hand is occupied by that target; in other words, in order to use both your hands for a 2-handed weapon attack or other purpose you must release the target.
There does remain some ambiguity as to whether that actually ends the condition though. The sentence in question states:
But there isn't a strict connection indicating that "release the target" is an additional thing, not part of the set specified by the condition, which ends the grapple. It does seem likely that it was intended to be so based on the juxtaposition of the concepts, and supported by the subsequent section which unambiguously states that the means of ending a grapple are not entirely restricted to those specified by the condition.
Regarding "Common sense"
In a comment you mentioned that you don't bring real-world common sense into D&D, which is fine. Sometimes the rules explicitly contradict reality; after all you can't complain about someone casting a fireball on account of "magic isn't real". However, D&D also isn't a computer Rules Enforcement System where ambiguous edge cases have a single answer that's always correct and non-negotiable. Instead, D&D is adjudicated by Some Guy who, in my experience, is much more likely to be swayed by "It doesn't make sense that my Half-Orc Barbarian is physically incapable of throwing a gnome" than by "the rules don't say that letting go stops the grapple"; your mileage may vary depending on the DM. In general, I would say that ambiguous situations not clearly covered by rules are more likely to take whichever interpretation most closely matches common sense even if other times common sense is ignored.