General Relativity Lagrangian

The Lagrangian density for the $h=h^{00}$ term of the Einstein gravity tensor can be simplified to: $$L=-frac{1}{2}hBox h + (M_p)^ah^2Box h – (M_p)^b h T$$ The equations of motion following from this Lagrangian looks roughly like (I didn’t calculate this, they are given in the problem): $$Box h = (M_p)^{a}Box(h^2)-(M_p)^bT$$ For a point source $T=mdelta^3(x)$, solve the equation for $h$ to first order in the source $T$, with $M_p=frac{1}{sqrt{G_N}}$. This result should reproduce the Newtonian potential.

Attempted Solution:

So to first order, we can drop the $h^2$ term and we are left with $$Box h = -(M_p)^bT $$ $$h = frac{1}{Box} (-(M_p)^bT)=-(M_p)^bfrac{1}{Box} (T)$$ where $frac{1}{Box}$ is the propagator (Green function) associated with the field. Based on some calculations and properties of the Green function I got $$h=-frac{M_p^b m }{4 pi r}$$ I am pretty confident of my calculations so far. Now, to actually get Newton potential I need $M_p^b=4pi G$. It is not mentioned, but I assume $G_N=4pi G$ so the only thing I have to show is that $b=-2$ to reproduce the classical result. I just don’t get that value… I tried to do a dimensional analysis of the Lagrangian, and I have $[L]=4$, $[Box] = 2$ so $[h]=1$. As T is the stress energy tensor $[T]=4$ and $[M_p]=1$ so we are left with $b=-1$ I just don’t know where I am missing a factor of 2. Also, assuming my calculations above were wrong, the whole time $(M_p)^b$ was just a constant so that should be the same, regardless of the rest of the solution. So I guess I am doing something wrong with the dimensional analysis. Can someone help me please?