http://www.southwest.com/assets/pdfs/corporate-commitments/contract-of-carriage.pdf
Section 7 (Baggage) e 3 says "Travel Equipment for Infants and Small Children. One stroller and one Child Restraint Device (car seat) per fare-paying Passenger will be conditionally accepted as provided in Section 7h without charge and will not count toward a Passenger‟s free Checked Baggage allowance."
Section 7h says "Conditional Acceptance
Carrier may, at its sole discretion, but is not obligated to, conditionally accept the following categories of items for Carriage as Checked Baggage subject to the Passenger‟s assumption of risk for damage to or destruction of such items. Checking items in the condition described below is considered by Carrier as Passenger‟s agreement to this assumption of risk.
(1) Fragile or perishable items
(2) Previously damaged items
(3) Improperly or over-packed Baggage
(4) Soft-sided cases or unprotected/unpacked items"
So it is officially at the passenger's risk. They can talk to Southwest and SW might do something for them as a goodwill gesture, but they are not required to do so. Frankly, especially with such "minor" (to their point of view) damage I would be surprised if they do anything.
If your neighbor continues to use the seat, make sure they know they must use the seat belt and not the cut LATCH strap. A tiny cut, in a crash, can cause the belt to rip right through.