I had turned in my MBP for repair at my school’s campus store and they claimed to have found water in it, and would cost $300 to repair the AppleCare+. I couldn’t believe it so I denied the repair but they charged $50 to give me the Mac back. I had turned it in to an Apple store a previous time and also charged $300, but nothing to deny the repair. Another reason why I shouldn’t go to 3rd party repair places?!
No they cannot charge you money for denying repair, in my experience there has been no 3 party store that can dent request. One possibility is that you gave in your MBP and they ordered the parts for it and after you denied repair but seeing from your post that doesnt seem to he the case. So i would go and get my money back