The phrase "what does something have to do with..." is commonly used to question the relevance or connection of a certain topic or issue. There are numerous synonyms that could be used in place of this phrase, such as "what's the connection between...", "how does this relate to...", or "what's the link between...". These alternatives can help to convey the same message in a more intriguing or concise way. Other options include "what bearing does this have on...", "to what extent does this impact...", or "what role does this play in...". Using synonyms in writing or conversation can enhance communication and make it more engaging for the listener or reader.