The Texas Teachers Retirement System (TRS) Benefits Handbook states "the retirement date as either the last day of the month of application or the last day of either the two previous months. Termination and withdrawal from eligible service by the effective date and for one full month following the effective date is required for retirement. A member on paid or unpaid leave status is not eligible to retire." Social Security will allow the Government Pension Offset (GPO) exemption up to one full month after the retirement date Texas TRS uses if the individual works in a position that is covered by both Social Security and TRS and if the covered earnings will be considered in determining the pension amount.
For example, Mr. Smith, a Texas teacher, has chosen to retire in May 2004, making the effective date of his retirement on the last day of that month, the 31st. He works his "last day" of employment on June 15—within the one month "window." Mr. Smith will be able to avoid the GPO because this last day was in a position that is covered by both Social Security and TRS and the covered earnings are considered in determining the pension amount.
You may wish to contact your local Social Security office concerning your specific circumstances.
NOTE: Based on the enactment of the Social Security Protection Act of 2004 (P.L. 108-203, enacted March 2, 2004), the "last day" exemption to the GPO can apply only if: 1) the last day of covered employment is before July 1, 2004; or 2) the person applied for the Social Security spouse’s or surviving spouse’s benefit before April 1, 2004.
For more details on this change in the law, see the question on the Social Security Protection Act of 2004. This law generally replaced the "last day" exemption to the GPO with a requirement that the person work in a position covered by Social Security for the last 60 months of government employment prior to retirement.