Pat the thawed shrimp dry. Halve the tomatoes, mince the garlic and chop the parsley. Finely grate the lemon zest without the white pith, then measure 2 tablespoons lemon juice. Bring a large pot of unsalted water to a boil.

Cook the squid ink linguine according to its package directions until just al dente. Before draining, reserve 1/2 cup cooking water in a heatproof cup. Drain without rinsing; time this to finish as the tomatoes soften.

Meanwhile heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the shrimp in one layer and season with the salt and black pepper. Cook about 1–2 minutes per side, depending on size, until the flesh is pearly or white and opaque throughout. Transfer to a clean plate.

Reduce the skillet to medium heat. Add the remaining 2 tablespoons oil and garlic; stir for about 30 seconds until fragrant, without browning. Add the tomatoes and cook 4–5 minutes, stirring, until their edges soften and release some juice.

Add the drained pasta and 2 tablespoons reserved water to the skillet. Toss gently for 1 minute, adding more water a tablespoon at a time until lightly coated. Fold in the cooked shrimp, lemon zest, measured lemon juice and parsley; warm briefly without prolonged simmering. Divide into four portions and serve immediately.