Can I use Carecredit to pay on Rover?

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I doubt it, but you'd have to check with either Rover support or Care Credit support (probably both). To contact Rover, go to https://support.rover.com/hc/en-us/re.... The easiest way to find out would be to try booking a service and see if it goes through. I'm surprised Rover doesn't seem to have a list of accepted credit cards on any of their support pages, from what I can see at least.
The reason it might work with a vet facility and not Rover is because your vet's boarding would be listed as a veterinary service for Care Credit, whereas Rover wouldn't be.
Good luck!