We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the fractal boundary Γ of a domain Ω in ℝ2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+−G21−, where the components G21± are extendable to H-monogenic functions in the interior and the exterior of Ω, respectively. H-monogenicity are a concept from the framework of Hermitean Clifford analysis, a higher-dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. H-monogenic functions then are the null solutions of a (2×2) matrix Dirac operator, having these Hermitean Dirac operators as its entries; such matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.