Hi Austin,
I have been in the tax search business in NJ for 20 years and I feel your pain. First thing I would do is ask the customer if they had a tax searxh completed prior to the closing. A separate tax search is normally mandated in a NJ closing. If they have a search, they should be relying on that and not coming to you for the claim. Next, if you feel you need to settle this with your client to perserve the relationship, you would only be responsible to any outstanding taxes up to the date of the closing. Anything after the closing ( even if it is in the middle of the quarter) become the responsibility of the new owner.
A word of caution, this outstanding tax is acruing interest daily, therefore the sooner you can get this resolved the better.
If you would like to call me for any additional information, feel free. I can put you in touch with my claims administrator who may be of some help to you. 973-323-8201.
Amy