I agree with noglider that they are worth saving. They look to bit Nitto Olympiads. Nice comfortable bars. The radius corners make for nice wrist clearance on the drops. The only visible part is at the stem and that looks fine. Little aluminum poilish on that and call that good.
I like the look of cloth tape but every one I unwrap doesn't look much better then yours. The cloth just holds the water and sweat and that's what you end up with.
I have had good luck with a scotch bright pad to get the chunks off and wipe down with something like disc brake cleaner sprayed on a paper towel to get any oils off it so the new tape will lay smooth and stick if you get the adhesive strip style.
Nice catch.