Bressler claims she has provided "extraordinary services" for the Jack Russell terriers - Cha-Cha, Dolomite and JJ.
A spokeswoman for Carey has so far not responded to requests for comment.
Carey is married to actor and producer Nick Cannon, and they recently welcomed a new addition to their household: a puppy named Jackie Lambchops, born to Cha-Cha this month, according to Carey's Twitter feed.
The Associated Press contributed to this report.
