Does it look bad to NOT apply/respond to Honors College Invitation?

No.

If he’s not interested don’t apply.

I agree with looking at perks - all Honors programs are different. So you want to understand b4 applying.

That said they likely send Honors apps to all or all who hit a statistical cutoff.

Some honors programs have cost. Some have scholarships. Can go either way.

Bottom line, if not interested, don’t apply and have zero concern.