It seems that the timer should have a switch to disengage the beeper.
If not, then you can open the box and locate the transducer (miniature speaker) and unsolder one of the wires and wrap the bare end of the wire with electrical tape or install a small thread-on insulating plastic wire nut.
That will remove the transducer from the circuit making the beeper silent. I've done this to a couple of similar devices and it did no harm that I could detect.
any idea or tips on opening up the 505? I tried, but so far, only chipped some plastic.