I didn't ask for specifics, but I know they were washed in the washer (with detergent). I think they were in the dryer too.
First off, I'm very much a skeptic on the hazards of submerging harness webbing in water, despite what it says in most of the manuals. I have handwashed harness straps in water, with a bit of mild detergent, and I will definitely consider doing this again in the future (if someone barfs on the harness, for example).
HOWEVER, having someone else wash the harness in the machine (unknown agitation stress, especially if it wasn't on gentle cycle), with unknown detergent and possibly other laundry additives, and then putting it in the dryer (unknown temperature and duration) would be beyond my comfort level. I would buy new harness straps for the seat. Oh, and double-check the routing of the harness... I don't think you said which seat it is, just that you are considering replacing it with a Marathon soon? Rethreading the harness can be tricky on some seats (ETA, just saw in you sig that it's a Snugride -- not much rethreading complexity there).
I think you asked whether it could wait until the Britax sale. Personally, I probably wouldn't. The sale is at the end of the month, isn't it? And then there's still an additional wait for delivery time. Also, unless you were planning to throw away your current seat, wouldn't it be better to have completely trustworthy straps on it, for any possible future use?
Katrin