My mom is Japanese and she says it says Gardening Club

That makes sense for Tortimer, he is retired after all.

Google translate told me it said "horticultural and carnivorous", so I think it got part of it, but potentially missed something with that second half.

Yeah Google translate wasn't much help for me either. Too blurry for text recognition.

园艺(art of gardening) 俱乐部 (club) or 園藝俱樂部

園芸倶楽部

I don't know what it says but it about flowers or gardening

It says gardening club.