The squeak is caused by high frequency sticking & releasing & sticking & releasing of the pad against the rotor. The noise comes from the steel backing plate of the pads against the cast iron of the caliper. New pads and cleaning the rotor work. If the pads still have ample material, they can be removed, very lightly sandpaper the glaze off the pad material, put anti-squeal goop (either rubbery stuff or brake caliper lube) on any shiny spots where the steel plate has been rubbing. Sandpapering and washing the rotor with brake cleaner is also a help. It happens in reverse because that direction of rotation moves the pads to a slightly different spot in the caliper.