I've been using Esbit for years and have not noticed enough suet to be concerned. It just wipes off, a little discoloration left behind but I don't care. Have you experimented with pot height from the fuel tab? Sounds like it might be too close.
Regardless, a little sand/dirt scrub will clean your pots in the field.
Wood fires leave a black residue as well. I just wipe/scrub it off with whatever leaves/dirt/sand/gravel is around me and pack it up.