A counterterm insertion on the photon propagator that absorbs the vacuum polarization divergence. Related to charge renormalization: the Ward identity ensures $\delta Z_1 = \delta Z_2$, so the charge counterterm is determined entirely by $\delta Z_3$.
The computational chain
From diagram to number—every step of the amplitude calculation.
The diagram
An X on the photon propagator — the photon field strength counterterm $\delta Z_3$. Absorbs the vacuum polarization divergence.
Feynman rule
$$i\Pi_{\text{ct}}^{\mu\nu}(k) = -i\delta Z_3(k^2 g^{\mu\nu} - k^\mu k^\nu)$$
The counterterm has the same transverse tensor structure as the vacuum polarization — enforced by gauge invariance. The Ward identity prevents a photon mass counterterm: the photon stays massless to all orders.
Charge renormalization
$$e_{\text{phys}}^2 = e_0^2(1 + \delta Z_3) \implies \delta Z_3 = \Pi(0)\big|_{\text{div}} = \frac{\alpha}{3\pi\epsilon}$$
The photon field counterterm is directly related to charge renormalization. The Ward-Takahashi identity enforces $\delta Z_1 = \delta Z_2$, so the entire charge renormalization is determined by $\delta Z_3$ alone. This is why QED has only three independent renormalization constants.