It is not possible to reset the ID Counters for your CMS. The reason the Counter ID is exposed is for Debugging and Troubleshooting, it cannot be altered.
I have included a link to the Documentation for the Tidy Library functionality:
The Tidy Library feature can be used in 2 ways: from the Settings option when logged in as a Super Admin or in the Media Library as any User. Can you confirm if you are logged in as a User or Super Admin when using Tidy Library?
If you are logged in as a non Super Admin User, please note that to be able to remove files using Tidy Library, the Logged in User must be the Owner of the Files. The Files must also not be in use on any Layouts or Campaigns and not assigned to any Displays or Display Groups.
Can you also confirm that the User you are logged in as is the Owner of the files and that they are not in use with any other Layouts, Campaigns, Displays or Display Groups?