My sister is quite sick and there are multiple goyim (catholics) asking to “pray” for her. Is it permissible to let a goy pray for a yid’s refuah shlemah?
You do not have any obligation to stop them from praying for your sister. To ask them them to pray for her wold depend on who exactly they are praying to, if it is to H-shem then it is fine, however if it is to an avoda zara, you should not ask them to pray for her.
May H-shem send your sister a refuah shleima b’m’heira!!