BackService popup Won't go away after device transfer

After a not so smooth transfer from old Macbook Air to new one, the minute I finished the transfer, I got a pop up "BackService" Not Opened - Apple could not verify “BackService” is free of malware that may harm your Mac or compromise your privacy.

I have read previous posts and done everything that was suggested and that I am capable of doing - to no avail. Regardless of which pop-up response I submit (Done or Move to Trash), it just keeps coming back up. I have searched EVERYWHERE for anything related to BackService and found nothing and have deleted anything and everything that isn't Apple product or something mainstream.

Running Sequoia. Brand new Air. M3.

I just don't know what to do...