Am I liable to bear costs for material and labor to redo flooring if a homeowner is unsatisfied with my original installment of brick pavers?

The first question is, did you offer the homeowner any sort of guaranty or warranty of the work? For example, "you don't pay until you're satisfied?" If you did offer such a guaranty, you are bound by its terms.

In the absence of a guaranty, while a homeowner has a right to receive commercial-quality work--e.g. if, broadly speaking, you don't provide what the homeowner commissioned or paid for, he does not have to pay. However, you are not obligated to take the homeowner's assertions at face value. If you agree that the work is not good enough (or not what he or she requested), then  you probably need to pay for labor and materials both--if you are sued by the homeowner for damages, or if in a different situation, the homeowner withholds payment and you sue to get it, if the work truly is below acceptable standards, then you will most likely lose.

On the other hand, if you believe the work is of fully commercially acceptable quality and comports with what the homeowner commissioned or hired you to do. you are not obligated to redo the work simply because the homeowner wants you to--and if you are not paid, you may sue for payment. If you end up in court--either because you are suing for payment, or in this case, because the homeowner is suing to try to recover money from you (after you refused to redo the work), there's a good chance you'd win.

Of course, you and the homeowner could legitimately differ on how good the work is, whether you need to replace it, etc. Since litigation is expensive and uncertain, it may be best for both of you if you can work something out. For example, if the homeown will pay the cost of materials, would you be willing to put in the time for free? That  might be the best outcome.