I can't really see that they are burnt from you photos. If they were damaged, the unit would not work. As you stated, they are part of the inverter circuit. Your unit would not be able to go into backup battery mode without these. It would likely trigger an error as well if they were shorted. These units typically have the ability to sense internal shorts. But if you can clearly see they look burnt, I would suggest replacing them. These MOSFETs can take a lot of abuse over time. They handle large amounts of current which is why they are adhered to such large heatsinks. But as I said, as long as you've resolved this potential issue, and gave the PCB a thorough inspection (replacing other potentially out of spec components like electrolytic caps) there's no reason why you shouldn't be able to rely on this for daily use. That being said, this is a more general statement. I am not too familiar with Tripp-Lite's UPSs. Do some research on this model. If there's a known failure mechanism (like I've ecountered with some APC UPS brands), then maybe switch to a different product.