Do they make faucets where the handle can't be removed to repair it? I'm trying to fix a leaking 20year old Grohe lavatory faucet and there seems to be no screw under the decorative cover.

It is a repairable faucet. Why are you repairing a 20 year old faucet?

Look around back for a screw. I think our old kitchen faucet was that way. I decided to replace it rather than fix it. It was a cheap old one and had nothing else that matched it. The new one is Moen.