Can I tile over a horizontal band of tiles in my shower?
I would not try to tile over the band of small tiles for several reasons. You said they were tight and what ever the gray material is your grout renew won't stick so that would be a problem with any new tile also. If you add a layer and it sticks you Now have a ledge that can hold water even if a grout filet was placed on the top edge there would be more of a chance of water getting trapped and the soap scrum that would collect would always be a pain. Last it would not look right, you would be better off carefully removing the band and replacing with the subway tiles you wanted to put on top.