First, your house is your homestead if you live there and own the home. As your homestead, the general contractor (known as the "original contractor" under Chapter 53 of the Texas Property Code which governs mechanic's liens) would have to comply with specified homestead lien requirements to perfect a homestead mechanic's lien contract. For example, the original contractor would have to have a written contract, signed by the owners of the home (husband and wife), record the contract with the county clerk, and insert various homestead warnings in the contract (among other requirements). Since you indicate that that did not happen, no one can file a valid mechanic's lien against your homestead.
Again, if the original contractor did not comply with the homestead mechanic's lien requirements, then neither the original contractor nor any subcontractor or vendor to the original contractor may file a valid mechanic's lien on your property.
Also, you may have other defenses. For example, if you had paid the original contractor before you received notice of non-payment from the subcontractor, and you did not make payment thereafter, then the subcontractor would not have trapped any funds in your hands. Under Chapter 53, you as the owner can only be liable for two kinds of claims: (1) funds trapped in your hands by a claimant's funds trapping notice; or (2) a retainage claim. You only need retain 10% of the funds paid to the original contractor if there is a proper homestead mechanic's lien contract, and then only until 30 days after the project was fully completed.
If you owed no funds to the original contractor after you received notice of non-payment by the subcontractor, you may not owe any money to the subcontractor. You should check with a construction attorney for an assessment of your legal position. In addition to filing a mechanic's lien timely, the sub has to provide a funds tapping notice by the 15th day of the second month after the month in which it performed the unpaid work. Without such notice, the attempted lien is again invalid.
When the sub filed its mechanic's lien, the sub was required to provide you with notice of lien filing within five days of the filing by certified mail. If you did not receive notice by certified mail, the lien is again invalid.
With no homestead mechanic's lien contract, you should write a letter by certified mail to demand that the lien be released, pointing out that the property is your homestead, and that the original contractor did not perfect a homestead mechanic's lien. If the sub does not voluntarily release the lien, he could be liable for a fraudulent lien under Chapter 12 of the Texas Civil Practice & Remedies Code. Chapter 12 can award damages of $10,000 or actual damages whichever is greater, plus attorney's fees.
You can also demand that the lien be released under Section 53.160 of the Texas Property Code, which provides for a summary procedure (no trial necessary) for the removal of an invalid lien on someone's homestead.
I have a lot of mechanic's lien materials (the law, notice forms, deadline charts, etc.) at my web site, The Construction Report. The web address for The Construction Report is:
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The sub will be required to prove the amount of the debt. I expect Texas lien statutes provide for you to move for a hearing to release the lien. I suggest that you do so and both the general and the sub will have to testify as to the claim. Then you will pay the appropriate amount and deduct it from what remains of the general's contract.