The Triangle Removal Lemma states that any graph with $o(n^3)$ triangles can be made triangle-free by removing only $o(n^2)$ edges. More generally, the Graph Removal Lemma states that for any graph $H$ on a constant $|V(H)| = k$ number of nodes, any graph with $o(n^k)$ copies of $H$ can be made $H$-free by removing at most $o(n^2)$ edges.

These theorems are proved using essentially the same set of techniques. However, I wonder if there is a *direct* proof of the Graph Removal Lemma, assuming the Triangle Removal Lemma, that does not need to pass through any of the usual regularity lemmas used to prove these things.