A proviso is entered on the waybill when goods are damaged.
This is a qualified acceptance, that means that the customer has accepted the goods but with a qualification owing to the fact that the goods are damaged or incomplete. This will have repercussions, for example, he will claim a discount or not pay the full invoice. I think you could use "conditional" or "qualified" acceptance but maybe "qualified" is better because "conditional" suggests to me this is an agreement prior to delivery