Yup, clean up the mess.
Oh you mean, I get it.
You will need someone to walk on the stairs, mark where you here the squeaks, and shim with wood wedges you buy or make. Then glue them in with a "gorilla" glue wood be my suggestion. Polyurethane glues will expand a bit and fill the voids.
Let it dry, so do this in the morning and go away for the day or night.
You could also try screws from the back, but be carefull not to go through the tread or split the wood, it makes more squeaks.
Post a picture if you can.