~てもいいです

I'm practicing this structure give/ask for permission and it occurred to me that it might have some relation to いいです, as in the adjective いい+です. Could this be the case? It's just personal curiosity

Edit: it came to mind while doing a listening exercise, in which the girl seemed to make an ever so slight pause after ても.

Yes, it is structurally て form + も + いい.
You may occasionally see ~てもよい as well.

Thanks