Actually, you can get rid of them without losing the rest of the POIs... with a caveat.
(Note: this is for my 7710, hopefully your 7725 is the same.)
1) Connect your RM to your PC using the USB cable but do NOT have the docking software running.
2) Your PC should mount the RM as a disk drive and give you the option of viewing the files on the RM.
3) Open the RM in File Explorer. You should see several folders and files.
4) Doubleclick on the "RM" folder, then the "Data" folder.
5) Locate the PetPOI.DB file and simply delete it.
Now they won't show up on your map but you will still have your other POIs.
The caveat: any time you update your RM (with construction info, new maps, running the Diagnostics etc) it will reinstall the PetPOI.DB file and you'll have to go back in again to delete it. However it is not that difficult because when you finish an update you can go directly to your File Explorer and you should already see the GPS mounted as a disk and follow the above steps at that point... no need to unplug/replug etc.