Thanks guys and gals

I'll try the WD-40 and hope it will not dissolve the box LOL.

Actually, hot water , detergent , and some rough stuff may remove the stuff, but the box itself isn't sturdy enough to take that rubbing. It will break before it can be cleaned. This is why I want some solvent to melt the gum away without much physical rubbing.

In the dollar stores around me we have great drawer type plastic organizers , but this is a box-type which is smaller and better for all sort of screws and other stuff.