What would cause a squealing noise on a manual transmission when I let off of the gas it goes away when I step on the gas again?

A squealing noise when you let off the gas in a manual transmission vehicle could be caused by a few issues. It might be related to the clutch release bearing, which can make noise when it's under load and quiets down when the clutch is engaged. Another possibility is a worn serpentine belt or tensioner that may slip when the engine load changes. It's advisable to have a mechanic inspect it to prevent potential damage.