RF modules flickering
The receiver has what is called automatic gain control (AGC). It basically amplifies everything it receives to a stable level, and when the transmitter is off, there is no signal and it amplifies the received noise to a stable level and this is what you see on output pin.

Unless there is no output for a received signal strength indicator (RSSI) that you can use to pass the received signal to LED only when the received signal is strong enough, there is not much ways of keeping the LED off.

Be aware that these types of modules usually do not work well or at all with constant input like you are using them now. They basically require that the transmitted data has transitions and on average 50% high and 50% low. Easy job for microcontrollers to use something like manchester coded data packets to transmit commands reliably to set LED state on or off.