You should really use find instead.

find <dir> -iname *.zip

Example: to search for all .zip files in current directory and all sub-directories try this:

find . -iname *.zip

This will list all files ending with .zip regardless of case. If you only want the ones with lower-case change -iname to -name

The command grep searches for strings in files, not for files. You can use it with find to list all your .zip files like this

find . |grep -e ".zip$"