Hopefully you have hired a real estate Attorney and have a great agent to help you. Congratulations on your sale!
You actually should be paid through August 1st at this point and you should be receiving a 20 day credit for taxes paid. You will see this on the HUD settlement statement as prorated taxes.
The problem is if you try to pay it now your payment will get lost in the shuffle. Co-ordinate with the closing attorney the best way to handle it. This is not an unusual scenario for them at all.
Payments of taxes, HOA fees, assessments, fuel oil, etc. are normally pro-rated. This means that for those expenses that are paid which cover a period of time beyond the closing date, you would receive a credit for these expenditures at the closing.
Your best avenue for good information on this is likely via your closing agent. Contact your attorney or title company for a clarification.
The closing attorney will divide up and portion the payment out on the HUD 1 closing statement.
Don't pay the bill as the attorney will handle as part of closing duties.