In general, if jars are improperly processed or don't seal, you reprocess them exactly the same way you did the first time. This doesn't depend on the original recipe; you just have to do the exact same thing over again. In your case, since it sounds like your original process was hot pack, you would have to open the jars, dump out the salsa and reheat it, resterilize the jars, and reprocess.
But in your case, unfortunately, it's too late. If you didn't process it long enough the first time, you have to assume that it wasn't sterile, and treat it as equivalent to not canning it at all. Yes, probability-wise, your situation is safer than that, but you have to plan for the worst case, because you have no way to tell. Something may have grown in there. Canning just isn't a good place to mess around with safety.
And before someone chimes in and says it, yes, if you're the kind of person who eats things that have been left out way longer than is reliably safe, you could save it. It'll work out some fraction of the time, so there are plenty of people out there who can truthfully say "I've done this and never had a problem." But it could also get you sick, so I can't recommend it.
I know the inversion method doesn't involve a water bath, you simply fill the jars, put the lid and band on them, and turn them upside down. There's question on how safe that is. (I know you didn't do the inversion method, but it's close even if by accident.)
I know marmalades can take up to two weeks to firm up and if they don't by then, it's suggested to reprocess them. At this point, I would say you would be safe to reprocess them. I wouldn't put what you have directly into a water bath though. I would pour the contents back into a pot and bring to a boil. Meanwhile, wash the jars and bands and use new lids. Then fill the clean (hot) jars and put into a water bath.
Best Answer
The conservative answer is that you should only do canning based on an approved, known to be safe recipe from a reputable source such as a university extension or a safety agency.
Having canned the salsa without the sugar, you have deviated from such a trusted recipe, and so the contents of the jars has to be considered at risk, as the sugar may have been a part of the reason the contents was safe or required less processing time than it otherwise might have (sugar in solution reduces the biological availability of the water).
This is especially true if the salsa was not made to have a pH of less than 4.6, to qualify as a an acid food.
Therefore, you should not adjust and re-process as the major ingredient may contain toxin.
Please see the information at the National Center for Home Food Preservation.