For the most part, there are limited opportunities for settlement of a comp claim. Once you have been determined at Maximum Medical Improvement (generally no more than 104 weeks from the date you started losing time from work), you will be assigned an impairment rating. For each % of impairment, you will receive 3 additional weeks of benefits. These have a lower maximum weekly payout than the disability (TIBs) payments you currently are receiving. Depending what you are receiving, the weekly benefit may, therefore, be lower. The impairment ratings are technical determinations by a doctor but, generally, the thumb tends to be more valuable than the fingers. In that respect, the thumb injury could result in additional benefits payments. Much of that depends on your response to further treatment. Hopefully, this will answer your question. You can contact the Division of Workers' Compensation ombudsman department to discuss the particulars of your claim. There are also a number of good attorneys in the Houston area who handle claimant's cases.
I think you should discuss this matter with an attorney licensed in Texas that is familiar with workers compensation awards and settlements. Here in Illinois, an injury like yours would probably merit a settlement of approximately 10-12.5% of a thumb, depending on the treatment rendered, the nature of the injury, etc.