Does undergraduate reputation matter for admissions?
Debatable. GPA probably counts a lot more than institution, but a lower GPA at a school known to be more difficult may not hurt as bad. Class standing might be a good indicator (I was top 10% with only a 3.6).
Some schools are known to be grade inflators as well. A big name behind you doesn’t indicate you’ll do well in med school either. I know 2 Ivy League grads who had to repeat a year of med school (one of them passed anatomy on 3rd attempt). Med school is a different beast than undergrad and anyone from any institution can struggle with it.