  We study flat Friedmann-Lemaitre-Robertson-Walker cosmological models for a
scalar field coupled nonminimally to teleparallel gravity with generic coupling
and potential functions. The goal of this paper is to determine the conditions
under which the cosmological evolution tends to the limit where the variation
of the gravitational "constant" ceases and the system evolves close to general
relativity. These conditions can be read off from the approximate analytical
solutions describing the process in matter and potential domination eras. Only
those models where the GR limit exists and is an attractor can be considered
viable. We expect the results to hold in the original "pure tetrad" formulation
as well as in the recently suggested covariant formulation of the teleparallel
theory. In the former case the GR attractor simultaneously provides a mechanism
how cosmological evolution suppresses the problematic degrees of freedom
stemming from the lack of local Lorentz invariance.
