How to clean burnt food from an unglazed tagine

You might try cooking it loose. Heat it up with plain water inside, even to boiling, and the combination of heat and soaking should loosen everything and make it easier to scrub out - especially if you scrape the bottom and stir occasionally as it boils.

Baking soda might help, sure - you might try hot vinegar and baking soda, boil vinegar and water, add baking soda, and let soak for a few hours. Or you might try a baking soda paste, leave on stubborn stains a while and try cleaning afterwards. Both possibilities are used for cleaning burnt food on pots, but it should also work for a tagine - I found one example of simmering hot water and baking soda in the tagine, which is another option.

Steel wool should be fine, though if you are worried about wear on the bottom of your tagine you can plan to use it infrequently, only for serious messes. Clay is pretty hard stuff, so it shouldn't actually be a problem (I use steel wool on my tagine, and the unglazed portions don't show any wear), but if you are worried just remember to scrub gently and let the abrasion slowly wear the residue away, instead of scrubbing hard. Other brushes and scrubbers should also be fine, though you might want long handles or heat resistance if you're going to pair scrubbing with simmering the residue soft.

Also, from what I've read, unglazed tagines are supposed to be seasoned with oil - not quite like cast iron, it involves soaking thoroughly, coating with oil, and heating at a low heat so the evaporation of the water pulls the oil into the pores of the clay. If your tagine was seasoned, it should be able to stand surface washing with soapy water - the danger is if the soap soaks into the pores of the clay, which an oil seasoning should prevent, especially if it's a brief wash not a prolonged soak and you rinse well. Up to you if you want to risk it or not, but it might help.

As a side note, there's nothing wrong with soaking a tagine...seasoning one requires prolonged soaking, in fact, and many sites suggest it for stubborn cleaning. I'm not sure what was said to GdD, but I've never heard anything against soaking.

If it is only the old cooked food you are trying to get rid of, try one of those natural degreasers.. I would first you lemon juice or vinegar and see about scraping it off with a flat wooden spatula. Home Depot sells a product for stoves and such called Zep Heavy duty de-greaser. Contact the manufacturer and see if you can use it in this way and then clean the tangine before you cook in it again.