Once you agree to arbitrate a claim, your rights to challenge an award are limited under the law. You could file a petition in court to challenge the award, but the grounds are limited. It does not appear that you have grounds here. Even though the contractor has not paid the window cleaning company, it was invoiced for the work and is still legally responsible to them. As such, you would not have a right to challenge the award just because the window bill was not paid.
Overturning an arbitration award is very difficult. Only limited statutory reasons are available. Hard to say without all the facts. If the award is large enough you can have an attorney evaluate.
Under California Bus & Prof. Code 7085.5(s), upon written application of a party to the arbitration, the arbitrator may correct the award upon the following grounds: (1) there was an evident miscalculation of figures or an evident mistake in the description of any person, things, or property referred to in the award; or (2) there is any other clerical error in the award, not affecting
the merits of the controversy. An application for correction of the award shall be made within 10
calendar days of the date of service of the award by serving a copy of the application on the arbitrator, and all other parties to the arbitration. From the facts you've provided, it seems you've already taken this step and the arbitrator has denied your application.
Any appeal from the denial of the application shall be filed with a court of competent jurisdiction and a true copy thereof shall be filed with the arbitrator or appointed arbitration association within 30 calendar days after the award has become final.
Please be advised that this answer is for general informational purposes only. This answer does not constitute legal advice, and does not create an attorney-client relationship.
If you asked the arbitrator to correct the award, and he denied your request, then your only available option is to file a motion to vacate the award in Superior Court. Getting an arbitration award vacated is difficult and can be granted only under limited circumstances. I am not sure that the facts you post would be sufficient to overturn the award.
You should contact a construction or litigation attorney who can review the documents and give you a better estimate of your chances.