A delivery incident opens when the shipper, the person who received the delivery, or Metrobi support reports a problem with how it went, not with when it happened. If you don't want to contest it, tap I do not dispute on the card and it closes with the effect applied.
The shipper can attach a dollar amount to it: what the damage cost and what they'd like back, capped at what the delivery was worth. If you do want to contest it, it shows up as a card in your Inbox, with a chat underneath it.
This affects your payment, not your reliability or your on-time number. While the incident sits open, the payment for the whole delivery job it belongs to waits with it, so it's worth responding rather than leaving it.
Write what happened in the chat, the same as with any other incident.