It's not necessary to remove contacts if you receive a massage. The main reason they ask is because your face will be sitting in the face cradle and pressure will be on your eyes while your face is positioned there for part of your massage.
Some other reasons could be in case you develop any reactions to lotions, oils, or other products they might be using.
I have worn my contacts with every massage I have received, and have never had any complications. If your eyes are sensitive, you may want to remove them before a massage, but you don't need to.