>> I then have a routine that compresses them in order to save space. I want to use a maintenance plan to delete the zip files that are older than 7 days.
Since the backup files are compressed, SQL Server doesn't recognizes those compressed backup files and hence not able to delete the zip files more than 7 days.
you have two options:
1. Remove the compression so that SQL Server recognizes them as valid backup files and delete it by checking whether it is older than 7 days.
2. Write a logic to delete files older than 7 days on your own and add it at the end of your Maintenance task or some other scheduled activity.
Hope this helps