Does keeping Jalabhar Xho in the court harm Westeros’s relations with the current regime in the Summer Isles?

It could, but it depends on how likely they think the Iron Throne is to actually fund him. Chances are, the current regime in the Summer Isles prefers to have Jalabhar Xho kicking his heels in King’s Landing than trying to stir up a rebellion at home. So if I was the Summer Isles, I’d bung a bit of money to the Iron Throne just to keep him there.