Combine the bottled lemon pepper marinade and dried basil in a shallow dish or resealable bag; add the chicken breasts and coat evenly. Refrigerate to marinate at least 30 minutes or up to overnight.
Preheat a grill or a cast-iron grill pan over medium-high heat. If desired, pound chicken to even thickness for even cooking.
Grill the marinated chicken 12–15 minutes, flipping once, until an instant-read thermometer registers 165°F (74°C). Remove from heat and let rest a few minutes, then slice into strips.
While the chicken grills, bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente. Drain and keep warm; reserve a cup of pasta water if you want a looser sauce.
In a medium saucepan over medium heat, melt the butter. Add the minced garlic and cook about 30 seconds until fragrant.
Whisk in the flour and cook briefly until it bubbles and forms a roux, about 30–60 seconds. Gradually whisk in the milk and add the lemon zest. Continue whisking and cook until the sauce thickens slightly, about 3–5 minutes.
Stir the pesto into the sauce until combined. If the sauce is too thick, add a splash of reserved pasta water to reach desired consistency.
Toss the drained linguine with the pesto cream sauce until evenly coated. Top with sliced grilled chicken and scatter the chopped, seeded tomato over the pasta before serving.