For some gravity theory coupled to a scalar field $phi$, I obtain, in xAct, the equations of motion

$$mathcal{E}_{ab}=R_{ab} (nabla_{c}phi nabla^{c}phi) + 2 R nabla_{a}phinabla_{b}phi + 6 nabla_{b}nabla_{a}phi nabla_{c}nabla^{c}phi – 6 R_{bc} nabla_{a}phi nabla^{c}phi – 2 nabla_{a}nabla_{c}nabla_{b}phi nabla^{c}phi+ldots$$

I would like to systematically remove all the higher derivative terms of the scalar field $nabla_anabla_bphi$ 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.