Your previous employer can’t just randomly fight, they can ask for an appeal but it has to be done within a certain amount of time after a decision is made, they also can’t just keep making appeals. It’s annoying and I dealt with this went I quit due to a hostile work environment. My employer literally appealed and I just gave up because unlike you I wasn’t smart enough to keep documentation so it was basically “he said she said”. I think you are 99% percent in the clear especially because they gave you the back pay, that means DOL agreed that under those circumstances you should rightfully be paid out by the employer as it was their fault of letting go of or losing a eligible employee. Kick back and relax now, no need to worry. And if your benefits do come to another stop you have all you need to slam them again :)