It's not picking one over the other, it's simply using them as it finds them.
TVs normally scan from low frequencies upwards, and someone else has said that the unwanted transmitter has the BBC mux at a lower frequency than the one you want. So the TV find that one first and tuned it, then later it finds duplicates and has probably stored them up at 800 onwards.
That's about it. If you attenuate the signal too much then you'll lose the one you want.
EDIT: The idea is to reduce the weaker signal to the point where the tuner no longer picks it up - but without reducing the wanted signal to that point.
There are many variations. If an attenuator works then that's simple (you might only need it when tuning, of if you have a good wanted signal then you can leave it permanently in place.
For others, it's sometimes possible to unplug the aerial lead until the TV has passed the unwanted signals. This is the case for a friend where they get a poor signal from a local infill relay at channels in the 40s, then the good signals from the main transmitter (Winter Hill in our case) in the high 50s and 60s. So the simple answer is to unplug the lead, set off the full scan, then plug it back in when the search reaches around 50.
Some devices have a function to rescan only the muxes it already knows about - that's useful as it means it can pick up channel changes, without going and finding stuff you don't want from other transmitters.
I had a "help" call from a friend not long ago. She has a very nice telly with sensitive tuner which picked up Moel y Parc in Wales as well as Winter Hill. Consequently she got a full set of duplicates - including what she termed "Taff TV".As I didn't have an attenuator to hand at the time (and also hasn't figured out that trick) I sat down and manually removed the duplicates - a right PITA and I wish the "powers that be" would come down off their lofty cloud and realise what a hassle it is when they force a retune on people. The TV doesn't have any selective scan feature, and the two transmitters have muxes on frequencies that are interleaved.
