Scattering on an ultralow potential in an armchair graphene nanoribbon is studied. Using the continuous Dirac model and including a couple of artificial waves in the scattering process, described by an augmented scattering matrix, a condition is derived for the existence of a trapped mode. Threshold energies, where the multiplicity of the continuous spectrum changes, are considered, and it is shown that a trapped mode may appear for energies slightly less than a threshold and its multiplicity does not exceed one. For energies that are higher than a threshold, there are no trapped modes, provided that the potential is sufficiently small.