I should mention first that the backed up files are not physically stored on the GP app on the mobile device. Only thumbnails are stored there to reduce storage consumption on the these mobile devices which by their nature, usually do not have a lot of storage to accommodate hefty-sized media files.
You can delete files from AP and GP.
When you delete a file from AP, this file will not be deleted on GP. This makes sense because GP acts as a backup. Think about it, if you delete the source file, and this action is replicated automatically to the backup copy, the action defeats the purpose of a backup, doesn't it?
By contrast, when you delete a file from GP, be it on the iPhone or iPad or on the GP website, this file is no longer visible on GP because it is marked as "to be deleted" in GP. In 60 days, this file will be automatically and permanently deleted from GP trash.
If you don't want to wait 60 days for this automatic deletion in AP via GP, you can go to the GP app and tell it to empty the trash.
https://support.google.com/photos/answer/6128858?hl=en&co=GENIE.Platform%3DiOS&oco=1