I understand that you have a contract on a new construction home that will be completed in a few weeks. Being new construction, it would be very odd and rare to have old lumber incorporated into a new structure. The only wood/lumber under a tub is normally the floor joists and then the subfloor material. What you may be seeing is the bark edge of the joist which should not be a structural issue.
Have brought the issue to the attention of your builder? Your home will be going through a final Certificate of Occupancy inspection conducted by the local building inspector and you may want to request that the builder have the material in question approved at time of CO inspection. Additionally, your Purchase and Sale Agreement may have an inspection clause that provides you with the right to inspect the home prior to closing and there might be a remedy clause where you can put the builder on notice (in writing) about any problems you find and then they probably have the option to fix the problems OR refund your deposit and then they would be free to sell the property to others.
The question of if you can back out of the transaction is difficult to answer without being able to read your purchase agreement. You should ask your Buyer's Agent to explain your agreement terms to you. Better yet, your closing attorney would be the best person to give you legal advice if your relationship with your builder erodes.
I would encourage you to be open an honest with your concerns and you should give your builder the opportunity to remedy the problem if there is one. If they agree with you that there is a problem and then they fix it, you are buying a home from a builder who cares about his clients and his reputation. This is also a good sign that you should get good service from the builder in the future if you need warranty service after you move in.
Best of luck with your problem and I'm hopeful that you can resolve it and then enjoy new home ownership and all that it has to offer.
Greg Hanner, Broker, REALTOR, e-PRO