In chapter 7.1.1. in Tong's notes about String Theory could someone sketch how can I show the statements that he nmakes around eq. 7.5

That the addition of the counterterm can be absorbed by renormalization the wavefunction and the metric

How does he conclude from the renormalization $$G_{\mu \nu} \rightarrow G_{\mu \nu} + \dfrac{\alpha '}{\epsilon}\mathcal{R}_{\mu\nu} $$ that the beta function equals $$\beta_{\mu\nu}(G) = \alpha ' \mathcal{R}_{\mu \nu} \quad ? $$
This post imported from StackExchange Physics at 20141001 22:39 (UTC), posted by SEuser Anne O'Nyme