Can anybody tell mw how to erase remote controls from memory of the car so i can programe some new ones?

I can not program new remotes, i just get the car about 1 month ago, it comed with no remote and just 1 key, so i get 2 second hand remotes, they work fine on other cars but not with mine. I have a friend with the mazda ids diagnostic and he tryd to program them but the bcm says that the memory is full of programed remotes, it accepts one remote until i turn the ignition off, after that is gone the new remote and in memory are located the old remotes. I cald the nearest mazda dealer and they sayd that they are not programing old remotes just if i buy new one from them for a bunch of money