Dad is being told off for eating too fast and not leaving enough food for grandma and grandad. He replies:
「おう、これでも遠慮してるんだぞ。じいさんもばあさんも、どんどん勝つ手に食べりゃいいんだ。」
Even though it looks (bad) I'm holding back. Both grandma and grandad rapidly ????
I assume 食べりゃ is a contraction of 食べれば. "It's okay if grandma and grandad eat ...".
I can't understand the 勝つ手に part. I guess from the に that 勝つ手に is supposed to be an adverb but I can't make anything make sense that fits the context.
勝つ手
(katsute) means winning hand (in game), but in this context, it seems to be勝手
as the answer below suggested.