If the creature is unwilling then nothing happens
Dnd 5e operates on the principle that things only do what they say they do. Jeremy Crawford, lead rules designer for 5e, and known for adjudicating rulings on Twitter, has stated:
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules. (source)
See this question, for further reference.
Following this principle, if the designers had meant a School of Conjuration Wizard to be able to swap places with an unwilling creature, subject to a saving throw, they would have stated so in the ability description. So, RAW swapping places with an unwilling creature, using this ability is impossible.
Further support for this conclusion has been suggested by mxyzplk, in the comments:
...this is why the word 'Benign' is in the name. In 3.5 there is in addition a 'Baleful' Transposition that does operate on an unwilling subject.
And, if you try, you'll probably lose your action.
If a PC wanted to try and do this, then it would be up to the benevolence of their DM as to whether they either simply "realise on reflection that such a course of action is impossible", or they lose their action that turn by trying to do it unsuccessfully.
Xanathar's Guide to Everything is an optional rules source, but it provides details on what would happen when a player tries to Cast a Spell on an invalid target.
Invalid Spell Targets (XGtE p. 86)
... If you cast a spell on someone or something that can't
be affected by the spell, nothing happens to that target,
but if you used a spell slot to cast the spell, the slot is
still expended. ...
Benign Transposition is a class ability rather than a Spell, but it seems logical that a failed use of it would follow a similar pattern - your action and one usage of the ability would be consumed, despite the failiure.
Could you 'homebrew' transposing an unwilling creature as possible?
In your own game your DM is welcome to rule entirely as they like, and in that case maybe a Charisma save might be argued to be appropriate for the unwilling creature (similar to the spell Banish)? However I would personally advise against this ruling. I think it would add a great deal of power to this ability and probably unbalance it.
Both Misty Step and Dimension Door work unimpeded
Misty Step and Dimension Door, when cast on creature outside the barrier, do not affect or target creatures or objects within the barrier, and they don't affect an area. Furthermore, Globe of Invulnerability does not block vision (required for Misty Step), nor does it prevent targeting of points within it (required for Dimension Door). So it seems that nothing in the text of Globe of Invulnerability would interfere with either of these spells.
Other teleportation spells might be affected
Note that while the two specific spells in the question are not blocked, not every teleportation spell is guaranteed to get through. For example, suppose you cast Steel Wind Strike targeting only creatures within the globe. The relevant parts of the spell's text are:
[...] Make a melee spell attack against each target. [...] You can then teleport to an unoccupied space you can see within 5 feet of one of the targets you hit or missed.
If all targets are unaffected due to the protection of the globe, then you have not hit or missed any of them, because you have not attacked them. Therefore, you cannot teleport using the spell, since you have no valid targets to teleport next to.
So, it's important to read the text of the specific spell you want to use to determine what interaction it will have with Globe of Invulnerability.
Best Answer
This should be a second-level spell
You've carefully worded this spell so that it's really hard to use it offensively. It's quite difficult to use this to drop someone off a cliff, or into lava, because they get to choose which space they appear in. If you use it on an enemy, you've also placed yourself with melee range of them, and you'll provoke an attack of opportunity if you move away.
(We can make it harder to use offensively by including some text about "arriving on a surface capable of supporting it". The 3.5e conjuration school uses text like this.)
You can still use it to pull your ally out of an awkward spot, which is nice -- but the original misty step was an escape spell, and this misty hook variant isn't an escape spell any more, and I think that's a fair trade.
(Also, this is a spell that promotes teamwork, and I like it when characters use spells like that at my table!)
If you can get past an opponent's saving throw, for a second-level spell slot you could hit them with blindness or levitate or hold person. I think moving them next to your character is in line with those spells.
For the friendly version of the spell, I think it actually should be a bonus-action spell as well, so that you don't blow your whole turn on pulling your ally out of a sticky situation.
How's this: