[quote=saltydog] Paper leaves a trace of ash and plastic leaves nothing [/quote]
salty, I have always heard that one should not burn trash, food scraps, etc. but carry them out. One individual's small residue multiplied by that of others is enough to attract animals and habituate them to the campsite (and so they return again to the next camper who may not burn anything)
I don't know if there is a Forest/Park service reg about this subject, but this is the first thing I Googled:
[url=http://www.fs.fed.us/t-d/pubs/htmlpubs/htm04232327/index.htm]Don't burn trash[/url]
Aside from the trash issue, there are other options for the food residue.
(1) sump method. Drain any liquids onto a cloth, trapping the solids to carry out, allowing the liquid to flow through into a hole in the ground. Admittedly, this still leaves odors in the ground, so it is not an ideal solution.
(2)My ultralighter friend Dan does this: uses soot-free alcohol stove and a thin plastic bag-like material (that is heat-proof). Lines his metal cup or bowl, pours hot water onto dehydrated food, and after eating there is no clean up because he just wads up the plastic film and carries it all out. Leaves no trace, but does require certain foods types, and weight of alcohol fuel that I imagine you are trying to avoid by burning twigs.
(3) After any cooking method: Clean up with no soap, just hot water, clean out the cup or bowl with the hot water and your finger or spoon, and drink the residue. Most people find this disgusting but after a week on the trail it's not so bad, anything goes. I'll be doing this when we are there. We may see you this summer.
