。
I wonder if Robin has gotten picky and spoiled with food.
Literal
Robin [topic-は] palate [subject-が] fattened extravagant become-[past-た] [wonder-のかしら].
口が肥える ('one's palate fattens') is an idiom for developing refined or demanding taste in food — the mouth becomes 'fat' from too much good eating. 贅沢になった ('has become extravagant') reinforces the idea. のかしら is a feminine wondering/questioning ending — の (question) + かしら (I wonder). The tone is gently critical.