"Not even remotely interested" means "not interested at all". Use this phrase to emphasize that you really, really don't care about something.
The word "remote" means "far away". So "not even remotely" means "not even far away". If you're "not even remotely interested", it means that you don't have any interest, not even a small, far-away interest.
Some other words you can use with "not even remotely":
Aren't you even remotely curious as to what he's been doing all these years?
Don't you think it's even remotely possible that there could be intelligent life on other planets?