And the option other than the put was?
B offered to sell put options (to A) on it's own debt. That means that if A's bond position weakens in terms of market value, so will the put options that B sold. Both A and B face wrongway risk.
No it offered to sell put options on its own stock. If that weakens - implying weakening credit quality of B - put options will turn into money for A, hence increasing counterparty exposure for A in the moment credit quality of B is deteriorating ==> Hence, credit exposure and credit quality negatively correlated = wrong-way risk.