That may entail a visit to the County Courthouse. By law, Texas Birth Certificates are closed to the "general public" for 75 years beginning on the date of occurrence. You cannot obtain copies of any births, after 1938, without written approval of the person(s). Delayed certificates are filed to record births that were not documented initially. Usually, two persons with knowledge of those births will submit sworn affidavits in support of the certificates. If you have an ally in Gregg County, request he/she visit the courthouse to research the "birth index". Although the actual certificate(s) might be inaccessible, the indexes are "open to the general public". Every county has them and some even have separate indexes for delayed births. "Voice of experience", born in 1946 and birth filed as delayed in 1948. The transfer of data from written records to the worldwide web is fraught with errors. I've observed more than one marriage date for a couple in the same county. Often, the dates were less than 30-days apart.