No you're right, if you ever get a bite from a cat you need to get to the dr fast, they can give you horrendous infections if they puncture the skin, so you are absolutely right to discourage her. Just keep persevering with what you're doing, keep putting her on the scratcher , and if she runs back to bite you [cos it's more fun ] then put her down and ignore her. No more play if she gets too rough. She will get the msg if you are consistent.

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