In a large skillet, heat oil over medium-high. Add grape tomatoes, capers, anchovies, olives, and garlic; cook until fragrant and tomatoes soften, about 5 minutes. Add tomato puree and season with salt and pepper; cook 2 minutes (sauce will be separated).
Meanwhile, in a large pot of boiling salted water, cook pasta until al dente. Reserve 1 cup pasta water; drain pasta and add to sauce, tossing to combine and adding enough pasta water to create a thin sauce that coats pasta. Season to taste with salt and pepper, and serve immediately.
To turn long pasta like spaghetti into a tidy mouthful, use your fork to gather a few strands at a time. Rotate the fork against the side of the bowl until a compact ball forms. As you twirl the pasta, it will collect just enough sauce, making for the perfect bite.