The spell does say what happens.
...if the object is moved more than 10 feet from where you cast this spell, the glyph is broken, and the spell ends without being triggered...
I would apply this to breaking the object in half or scratching the glyph. As for it it being too easy to disable, keep in mind the glyph is nearly invisible. You're not going to spot it just walking past. You have to be looking for it, or at least investigating the area. It's not going to be easily found.
There's also the idea that you can set one of the triggers to be if the glyph is tampered with so it does go off if someone tries to disable the glyph.
A stored spell (probably) has the same range as the normal version of that spell
There is nothing in Glyph of Warding's text that explicitly states a maximum or minimum range at which it can cast a spell. The Range for Glyph of Warding itself is "Touch", but that is presumably to create the Glyph, not for effects the Glyph creates. The Glyph itself can "cover an area up to 10 feet in diameter", but that does not necessarily mean its effects are limited to this area.
There is a small hint in the text that the Glyph can effect things which are not touching it. Specifically, amongst the possible triggers it states (PHB, p. 245 bold added)
typical triggers include touching or standing on the glyph, removing another object covering the glyph, [or] approaching within a certain distance of the glyph.
However, this does not tell us definitively whether or not the Spell Glyph can cause effects at any particular range. After all, the the Explosive Runes version of Glyph of Warding effects things in a 20 foot radius sphere centered on the Glyph, so a trigger of "when a creature comes within 15 feet of the Glyph" would be a reasonable (if often sub-optimal) trigger for that feature alone.
The biggest hint we have is simply the description of what happens when a Spell Glyph is triggered (PHB, p. 246, bold added):
The spell being stored has no immediate effect when cast in this way. When the glyph is triggered, the stored spell is cast. If the spell has a target, it targets the creature that triggered the glyph.
The triggering of the glyph will cast the spell you stored in it, in your case Greater Restoration. The spell will have all the qualities that it usually does, including range, duration, and effects.1
If Glyph of Warding changed features of the spells it "casts", its text would say so. Since it does not, the Range of the stored spell most likely remains unchanged. So a creature would need to be touching the Glyph of Warding in order to benefit from a stored spell of Greater Restoration, since Greater Restoration's range is Touch. If the stored spell had a longer range, that range would be used instead. For example, if you stored the spell Haste into a Glyph of Warding, the Glyph could target any creature that triggered it with a Haste spell as long as that creature was within 30 feet of the Glyph (the range of Haste being 30 feet).
1: The only feature of the spell we can be sure will change when it is triggered (besides "concentration") is its components: the components are necessary for "casting" the spell (so you presumably needed them when you "cast the spell" as part of the casting of Glyph of Warding), but we are already told that "the stored spell is cast" when the glyph is triggered without any caveats (which is good, since the Glyph has no hands to gesture somatically or mouth to speak the verbal components). So the components will be unnecessary when the spell is triggered, the same way it would be unnecessary to pay gold for an item that a spell magically created, even though that item usually costs gold at a store.
Best Answer
Yes - You can cast metamagic-enhanced spells into a spell glyph (except for empowered)
All the metamagic abilities except empowered say:
So, because you are still casting the spell (per the description of spell glyph) and you can apply metamagic whenever you cast a spell per the metamagic description, I see no reason why this would not be allowed.
It is worth noting also that ring of spell storing which works in much the same way as spell glyph, specifically restricts the qualities that the spell stored in the ring can keep. Since there are no such restrictions here, the most straightforward interpretation is that the spells are stored exactly as the caster casted them (including metamagic).
Empowered spell is a special case that only works with the spell after the glyph has triggered
Empowered spell is the only metamagic ability that can (and RAW must) be applied after the casting of the spell has taken place. Thus, it must be addressed separately.
Thus, you shouldn't even need to apply this metamagic ability when you cast it, but can wait until it is triggered.
Can you cast an empowered spell into a spell glyph? - No
Empowered spell says:
RAW imply no, because you only apply empowered spell when you are rolling damage for the spell which means this takes place after a spell has taken effect.
And spell glyph says specifically that the spell's effects are delayed:
The reason that empowered is written like this is because it allows the sorcerer the chance to spend the points to use the ability only if damage is actually going to be applied. Thus, for example, an enemy making their save and taking no damage from your spell would not result in you wasting sorcery points.
So, RAW, you cannot cast an empowered spell and store it in a spell glyph.
Can you apply empowered spell to a spell after spell glyph triggers? - Yes
This answer depends on if the triggered spell is considered by your group to be cast by the sorcerer or if the glyph is considered to be a proxy for the caster. This is a matter that is not precisely clear RAW, and is talked about in this Q&A.
In the end, it makes sense to allow the sorcerer to apply the metamagic to the spell since they are the ones who cast it originally and the glyph is only acting as a proxy to cast it for them.
Allowing does enable some weird situations. For example, the remote nature of the spell would mean that you could be miles away or even on a different plane (thanks @Marq) from the glyph when it triggers. Allowing the spellcaster to modify the spell with empowered would mean that they could then modify the spell from basically anywhere, which many not make a whole lot of mechanical or thematic sense. But not everything in D&D5e fits perfectly together. Use common sense if you are DMing the situation and if you are the player don't expect the DM to allow you to do anything.
So, in the end, the easiest way to handle this situation would be to say that the spellcaster can apply empowered to the triggered spell.