Under Texas law if an employee is expected to be paid less than $75,000 annually then a background check cannot reach back more than seven years on criminal convictions in most cases. There are certain jobs that require or permit extended review, such as employment in the insurance business or jobs that perform in-home services or residential deliveries.
If you do not receive the job you have the right to request the reason and ask for a copy of the background check. That will let you know the extent of information the employer had access to in making their decision.
I believe that you are confusing the time frames for credit history and criminal history checks. Credit checks with the 3 large credit bureaus may list bad credit reports for 7 years and up to 10 years in some cases. Criminal history reports usually pick up all arrests and convictions of your criminal history record. Some records, particularly felonies, which are older than 10 years, may be expunged for certain purposes or removed from credit histories. However, you would have to see a criminal lawyer who could clarify that for you.
Unfortunately, if you have not removed certain convictions for credit checks, they will appear on a credit check. Good luck!
My response herein is an attempt to give you general information and direction and is not intended to constitute an attorney-client relationship as perceived by state law.