In what it claims is an industry first, HRG has decided to absorb the new GDS opt-in charges.
It was followed this week by UK independent Capital Business Travel which also said it would not pass on the charges to its customers.
The moves put the two TMCS out of step with UK rivals American Express and Carlson Wagonlit Travel (CWT) which have both announced they will pass the charges on to clients.
HRG said that is decision follows "clarification" of BA's latest contract negotiations with Galileo and Sabre.
The deal which the airline signed with these two GDSs as well as Worldspan make them BA's "preferred channels" for booking their flights.
But BA is levying a 50p surcharge on first, business and economy class bookings and £1 on bookings for its cheaper flights.
The agreements came into force on April 10.
Mike Platt, HRG's industry affairs director, said: "In recent years HRG has played a crucial role in working with the airlines and GDS suppliers to anticipate change and ensure that we have the most efficient and widest access to fares and ticketing alternatives for the benefit of our clients.
"We are also committed to maximising our clients' expenditure and creating added value whilst doing all we can to avoid passing on added cost as a result of industry developments.
"We therefore felt it appropriate to await further clarification from BA before setting out our position and I am pleased that we have now been able to avoid further charges for our clients.
"We will continue to monitor the situation to see how it develops in the future and will undertake a review of our position in 12 months' time."
Simone Buckley, managing director of Capita, said: "We are continually experiencing pressure on our operating costs from many different areas. Our role as a travel management company is to provide our customers with access to the richest content in terms of fare availability at all times.
"Capita Business Travel is continually striving to keep our operating costs as low as possible, without compromising service, in order to continue as a valuable provider in the chain of distribution.
"It is for this reason that we will not be passing on to our customers the additional fees being incurred to access BA travel content using Galileo."
* Talks between BA and Amadeus, the only major GDS not to have signed a deal with the carrier, are continuing.
A source at Amadeus said: “We are still in discussion. We want to reach an agreement and we believe that we will but we would prefer not to comment further at this stage.”
Amadeus has said it will absorb the £3 levy for bookings not made through preferred channels until next Tuesday (May 1) when it will review the situation.
* see BTE's recruitment site www.businesstraveljobs.com