We study singular integral operators induced by Calderón-Zygmund kernels in any step-2 Carnot group \(\mathbb {G}\) . We show that if such an operator satisfies some natural cancellation conditions then it is \(L^2\) bounded on all intrinsic graphs of \(C^{1,\alpha }\) functions over vertical hyperplanes that do not have rapid growth at \(\infty \) . In particular, the result applies to the Riesz operator \({\mathscr {R}}\) induced by the kernel \(\begin{aligned} \textsf{R}(z)= \nabla _{\mathbb {G}} \Gamma (z), \quad z\in \mathbb {G}\backslash \{0\}, \end{aligned}\) the horizontal gradient of the fundamental solution of the sub-Laplacian. The \(L^2\) boundedness of \({\mathscr {R}}\) is connected with the question of removability for Lipschitz harmonic functions. As a corollary of our result, we infer that closed subsets with positive \((Q-1)\) -Hausdorff measure (where Q is the homogeneous dimension of \({\mathbb {G}}\) ) of the intrinsic graphs mentioned above are non-removable.
