BCD TECHNOLOGY S.A.

Exhibit 10.5

BCD TECHNOLOGY S.A.

December 31, 2004

Davis Family Holdings LLC

Davis Family Holdings II, LLC

Norwood H. Davis, III

Dear Mr. Davis:

The letter agreement (the “Agreement”) grants Davis Family Holdings, LLC, Davis Family Holdings II, LLC and Norwood H. Davis, III (collectively, the “Davis Shareholders”), as well as an immediate family member, a trust (with beneficiaries of only immediate family members), or a family limited partnership (with general partners and limited partners of only immediate family members) of Norwood H. Davis, III who may become shareholders of TRX, Inc. (collectively with the Davis Shareholders, the “Davis Family”) the right to require BCD Technology S.A (“BCD”) to purchase shares of common stock of TRX, Inc. (the “Company”) owned by the Davis Family upon the terms and conditions set forth herein.

At any time after January 3, 2005 until the earlier of (i) the date of an initial public offering of the Company’s common stock, or (ii) the date immediately prior to the termination of Norwood H. Davis, III’s employment with the Company for any reason, the Davis Family may offer to BCD (or its designated affiliate if such affiliate is a shareholder of the Company) during the first month of each calendar quarter all or part of the shares of the Company’s common stock owned by the Davis Family (such shares offered to BCD referred to herein as the “Put Shares”) and BCD shall purchase the Put Shares. In order to exercise this right, the Davis Family must send written notice (the “Put Notice”) to BCD of its intent to sell the Put Shares which written notice shall include the number of shares of common stock to be sold and a proposed “Put Price” (defined below). The Davis Family may exercise its right to require BCD to purchase the Put Shares on multiple occasions until there are no longer any shares of the Company’s common stock owned by the Davis Family.

The price for the Put Shares (the “Put Price”) offered to BCD pursuant to this Agreement shall be equal to the amount which would be distributed to the Davis Family for such Put Shares upon the dissolution of the Company if the entire business of the Company was sold to a third party for cash at its “fair market value,” as defined herein. For purposes of this Agreement, “fair market value” shall be determined pursuant to the terms and conditions of the Amended and Restated Shareholders Agreement by and between the Company, BCD, Davis Family Holdings, LLC, among others dated May 23,2001, as the same may be amended from time to time.

The closing for the purchase of the Put Shares (the “Closing”) shall be within thirty (30) days after the final determination of the fair market value of the Company. Upon the closing,

Davis Family Holdings LLC

c/o Mr. Norwood H. Davis

Mr. Norwood H. Davis

December 31, 2005

Page 2

BCD shall pay to the appropriate member or entity of the Davis Family the Put Price in the following manner:

(i) if the closing occurs prior to November 17,2005, twenty-five percent (25%) by cashier’s check at the closing and seventy-five percent (75%) pursuant to a promissory note (the “Put Note”). The Put Note shall provide for payment in two installments, with the first payment due on the first anniversary of the closing in a principal amount equal to twenty-five percent (25%) of the Put Price, and the second payment due on November 17,2006 in a principal amount equal to the remaining fifty percent (50%) of the Put Price. The Put Note shall bear simple interest at an annualized interest rate equal to the yield of U.S. Treasury Notes (three-year) as published in the Wall Street Journal on the date of issuance of the Put Note; or

(ii) if the closing occurs on or after November 17, 2005, twenty-five percent (25%) by cashier’s check at the closing and seventy-five percent (75%) pursuant to a promissory note (the “Put Note”). The Put Note shall be for a term of no longer than one (1) year and shall bear simple interest at an annualized interest rate equal to the yield of U.S. Treasury Notes (3 year) as published in the Wall Street Journal on the date of issuance of the Put Note.

The Davis Family and BCD acknowledge and agree that pursuant to that certain Shareholders Agreement by and between the Company, BCD and Hogg Robinson Holdings BV (“Hogg”), as amended, in the event a shareholder offers to sell shares of the Company’s stock to BCD, BCD is required to cause such shareholder to offer such shares to Hogg on a pro rata basis with BCD on the same terms and conditions. Therefore, the Davis Family agrees that upon sending a Put Notice to BCD, the Davis Family will, at the written request of BCD, also offer to sell the appropriate number of Put Shares to Hogg or any other shareholder of the Company on the same terms and conditions.

This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

This Agreement shall be governed by, and construed and enforced in accordance with the laws of the State of Georgia (without giving effect to the conflict of law principles thereof).

Please indicate your agreement with the above terms by signing copies of this letter at the points indicated below.