You don't really have to bypass them. I think, but I'm not sure, that they are all licensed by the city for special taxi transportation services. Only six of them are licensed by the city for that. Those are:

COOTRAMO
http://www.cootramo.com.br/

TRANSCOOPASS
http://www.transcoopass.com.br/

TRANSCOOTUR
http://www.transcootour.com.br/

ROYALCOOP
http://www.royalcoop.com.br/index.html

COOPERTRAMO
http://www.radio-taxi.com.br/

COOPATUR
http://www.coopatur-radiotaxi.com.br/index.php?to=home

They all have regulated fares by the city's Department of Transportation.

From GIG to the city center, where the Ibis and SDU are located, the fare is R$ 76,00.

If you take the conventional taxi (yellow with a blue stripe) that runs with the taximeter, you only pay at the destination. They also have a fare table when the origin of the ride is either GIG or the central bus station.
From GIG to the city center, the fare is R$ 36,50 from 06h00 to 21h00, but from 21h00 to 06h00 it costs R$ 44,00. Not many cabs respect that fare. They usually start the meter anyway even though it's forbidden from GIG and from the bus station. It's not all that bad, since the fare ends up being almost the same.

If your relatives don't carry a lot of luggage, they could take the bus to SDU, from where they would walk to their hotel.

It's either Premium Auto Ônibus or Real Auto Ônibus on lines 2018, 2101 and 2145, but beware, because the line numbers are not shown on the bus displays. You should ask the driver. Just ask for Santos Dumont, which is better understandable for him. If you see a blue bus like this, it's one of the lines:



The only reason for asking is to make sure it's not line 2918.

http://premiumautoonibus.com.br/site/