I just bought some budget tyres from ebay that were listed as brand new tyres. The tyre company said they were remoulds. Is this legit?

An un-used remould is a "New (remoulded) Tyre" but if it didn't state remould in the advert, that's false advertising and I'd raise a claim with ebay

I only have one experience of a remould tyre, and that was being a passenger when part of the tread separated from the rest of the tyre at about 100mph and decimated the front wing of a mk3 capri. Since then I've never been a fan of them

If the add didn't mention they were remoulds you have a good case for a refund