For some gravity theory coupled to a scalar field $\phi$, I obtain, in xAct, the equations of motion
$$\mathcal{E}_{ab}=R_{ab} (\nabla_{c}\phi \nabla^{c}\phi) + 2 R \nabla_{a}\phi\nabla_{b}\phi + 6 \nabla_{b}\nabla_{a}\phi \nabla_{c}\nabla^{c}\phi - 6 R_{bc} \nabla_{a}\phi \nabla^{c}\phi - 2 \nabla_{a}\nabla_{c}\nabla_{b}\phi \nabla^{c}\phi+\ldots$$
I would like to systematically remove all the higher derivative terms of the scalar field $\nabla_a\nabla_b\phi$ and beyond, since there are many of this type in the ellipsis. I have tried with MakeRule but I didn't manage to find a suitable expression.