I think some of these suggestions are based on a perfect world that doesn't exist at DFW airport. By the time your folks actually arrive, (maybe late), get through the terminal, locate a cab, drive to Grapevine or Irving, get seated, fed, call another cab and get back to the airport, during rush hour, through security and to the gate even seconds before the door of their departing flight is closed, (assuming it is on time), probably means they can plan a leisurely evening meal at any of the places named since they may be spending the night.

I'd suggest a trip to the Hyatt Regency Hotel in the airport:

Mister G's
An incomparable dining experience at Mister G’s
Jacob's Spring Grille
Featuring New American cuisine with a regional flair

or any of the multiple places to eat in the airport terminals, (especially terminal D)

American
Bennigan's - D11
Cereality - C6
Champps Grill & Bar - D24
Chili's Too - B20, C16
Cool River Cafe - D25

Fuddruckers Hamburgers (Marche) - D18
Reata Grill - D33 Upper Level
T.G.I. Friday's - A22, B10, C8, C29, D34, E17
Varsity Grill - E31
Asian
Blue Bamboo Xpress - D31

Manchu Wok - A25, C22, E15
BBQ
Cousin's Bar-B-Q - B27, D28
Dickey's Barbecue Pit - A18, C6, E12

Railhead BBQ (Marche) - D18
Cocktail Lounges
Cowtown Bar - A35
La Bodega Winery - A15, D14
Rider's World Bar - E15

Texas Stadium Skybox, Bar - A10, B6, C25
Tigin Irish Pub & Restaurant - D20
Coffee
Dunkin Donuts - A28, B7, D22, E6

Starbucks Coffee - A13, A29, A33, A37, B8, B14, B28, C6, C8, C21, C27, D25, E8, E31
Delis & Bakeries
Au Bon Pain, Deli - A13, A25, A38, B22, C22, C33, D27, International Arrivals (Outside Security)
Blimpie - C6
Camille's Sidewalk Cafe - D27

Einstein Bros. Bagels (Marche) - D18
Jazzman's Cafe - D10, D28
Subway - A33, B16
Desserts & Snacks
Auntie Anne's Pretzels - A25, A39, C12, C22, D12, D36, E15
Ben & Jerry's Ice Cream - D12, D27
Freshens Yogurt - B7, C6, C35, E6, E36
Grove Natural Snacks - A17, A39, C14

Grove Soda Fountain - D22
Häagen-Dazs - C17, E15
I Can't Believe It's Yogurt - A13, A25, A39, C22
Smoothie King - C14
Fast Food
Burger King - E6, E31
KFC - A25
McDonald's - A13, A25, B29, C6, C22, D33
Pizza Hut Express - A25, B10, C6, C19

Popeyes Chicken & Biscuits - A13, D22, E15
Taco Bell Express - A13, C14, E6, E15
UFood Grill - B8
Wendy's - C14
Italian
East Side Mario's - A38
Sbarro Italian Eatery - B5

Uno Dué Go - C33, E36
Mexican
360° Gourmet Burritos (Marche) - D18
Blue Mesa Taco & Tequila Bar - D31
Cantina Laredo - D27 Upper Level

Tequileria - A16, E12
Urban Taco - C22

South Texas? That's been a long time ago, but I recall a place in Harlingen or Wesleco
I believe was called Los Lomas where we ate frequently and there were numerous other hole-in-the-walls in McAllen, Brownsville and South Padre Island with brown meat sauce. I don't recall anything down there much different from the San Antionio, Austin, Dallas/Ft. Worth variety.
The only significant variation I know of is in El Paso where red and green, (not tomatillo), sauces reign supreme but that is so far west, it is more New Mex-Mex. (And lots better in my opinion).
I always figure Texas Tex-Mex applies to the stuff served in the strip from Brownsville to Amarillo about the width from Lubbock to Dallas with Corpus and Houston thrown in for
good measure.