Before and after I wipe down my corker with a paper towel sprayed with a water/sulfite solution. I will semi close the jaws to access the jaws themselves and even roll it up and punch it thru just like a cork. Do the underside too.
I do not apply the solution on as yes it will begin to corrode the frame. Merely wipe off well.
You may want to give it a real good warm soapy water rinse and dry real well and place near a heater vent or allow a little sunlight to warm and dry it well. If that doesn't work try some oxy clean.
It's probably has some left over drops of wine down in it. Definitely dry well when finished.