You should have received a warranty booklet for the tires with all the manuals. The warranty book for OEM tires is different than the warranty book for replacement tires. There is no mention of a mileage warranty. The tires are only covered for defects. See section 4.B. "Company does not offer tread wearout coverage up to a predetermined mileage under this Policy."
If you replace your OEM tires with identical Continental tires, those will have the 60K mile treadwear warranty.