depends on who you ask. one crusade was started after muhammed was recruited and funded by rome to sack jerusalem. he won but refused to hand it over to the romans.
Are you sure about that?
Isn't it the Rashidun Caliphate (the Islamic state established by Muhammad and led by his successors) that conquered Jerusalem from the Eastern Roman (Byzantine) Empire, and took it away from Roman control in 637-638 CE?
yes it is. that was what rome paid for. muhammad was at odds with jews, christians, and arabs because of his radicalism. he had little power until rome funded him. he took mecca then jerusalem. he was not popular but took jerusalem. it took centuries for rome to respond. The Antichrist Showdown! pt 26 - Islam [recruitment of Mohammed by vatican at 23 minutes] https://www.youtube.com/watch?v=ydGs4k5Tx7Q
that was what rome paid for.
Why would Rome pay Muhammad to take what already belongs to them?