To exclude files from the media library display you must create a pre_get_posts() filter the removes them from the list.
I don’t remember all of the details of doing this,, but it will require having some way to determine that the files were uploaded through the specific form. Possibly by creating a custom field for files that is set.
There are many examples of doing this, for example this one only shows files uploaded by the current user https://wordpress.stackexchange.com/questions/76771/how-can-i-hide-media-library-images-from-general-users
