Can my employer legally lower my pay for walking out of the store and quiting

He has to pay you what he agreed to
If you are saying he took you back and lowered your pay he still can not do that.
I would not accept going back unless he gave me a raise.

He has to pay for the time you worked. If you quit and want to come back he can rehire you on his terms.

If she is wanting to go back --his terms; but if he is begging her to come back then she has the upper hand