The wire is designed to be a rough quarter wave antenna. Better results are obtainable using a short coax cable to extend it ( solder core to the antenna point and shield to the board ground plane next to there) to a better antenna. A dipole at the end using the same length as the original connected to shield and centre will improve things, or you can get an antenna for those receivers that improves things.
Just note though that too much signal is no good, as the receiver is a superhet design, and too much signal will stop it working. Best is to just move the receiver out of the motor unit and mount it near the door on a non metallic wall. It likely is a single black box with 3 wires connecting it.