How to detect that my iPhone has been backed up with iTunes?

Solution 1:

Does that person know your passcode?

If not, then no.
You need passcode or fingerprint before the phone will trust the computer.

From comments - If they did know the passcode, there is no way to tell.
Giving someone your passcode or Apple ID password is almost the same as giving them your ATM card & PIN, if not worse. They can do what they like, because every system they interface with will think it is you.

Solution 2:

In general, this will be difficult on the phone itself since you’re trying to forensically reconstruct past events from log files that expire routinely. The easiest thing would be to take your phone to each computer you suspect and see if there’s a pairing record or backup stored on the filesystem.

Each phone makes it’s own folder, so you might see two phones backed up to a computer you only expected one.

A pairing and backup surely leave log messages on iOS, but since you can’t easily inspect those, you would need Xcode to open the console and read the log files from the phone.