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Nonlinear topological photonics has been attracting increasing research interest, as it provides an exciting photonic platform that combines the advantages of active all-optical control offered by nonlinear optics with the unique features of topological photonic systems, such as topologically-protected defect-immune light propagation. In this paper, we demonstrate that topological interface modes and trivial edge modes of a specially designed graphene metasurface can be coupled in a tunable and optically controllable manner, thus providing an efficient approach to transfer optical power to topologically protected states. This is achieved in a pump-signal configuration, in which an optical pump propagating in a bulk mode of the metasurface is employed to tune the band structure of the photonic system and, consequently, the coupling coefficient and wave-vector mismatch between edge and topological interface modes. This tunable coupling mechanism is particularly efficient due to the large Kerr coefficient of graphene. Importantly, we demonstrate that the required pump power can be significantly reduced if the optical device is operated in the slow-light regime. We perform our analysis using both \textit{ab initio} full-wave simulations and a coupled-mode theory that captures the main physics of this active coupler and observe a good agreement between the two approaches. This work may lead to the design of active topological photonic devices with new or improved functionality.