I'm not intending to suggest there aren't better solutions than periodically taping & cleaning, but a can of adhesive cleaner stuff will make short work of that mess, worth having.

(The one I use - mainly for barcode etc. stickers with shitty adhesive that doesn't peel off nicely - is by 'Pro Power' which I think is CPC's house brand, so that's not helpful if you're outside the UK.)