A counterterm insertion at the electron-photon vertex that absorbs the vertex correction divergence. The Ward-Takahashi identity enforces $\delta Z_1 = \delta Z_2$, relating the vertex and electron field renormalizations. This is why QED has only three independent renormalization constants, not four.
The computational chain
From diagram to number—every step of the amplitude calculation.
The diagram
An X at the electron-photon vertex — the vertex counterterm $\delta Z_1$. Absorbs the UV divergence of the one-loop vertex correction.
Feynman rule
$$-ie\delta Z_1\gamma^\mu$$
Same Lorentz structure as the bare vertex $-ie\gamma^\mu$, multiplied by the divergent coefficient $\delta Z_1$.
The Ward-Takahashi identity
$$\delta Z_1 = \delta Z_2$$
This is the most important identity in QED renormalization. It says the vertex counterterm equals the electron field counterterm — the vertex divergence and the self-energy divergence are not independent. Physically: the coupling of a photon to an electron is protected by gauge invariance, so the vertex renormalization cannot differ from the wavefunction renormalization. This reduces four potential counterterms ($\delta m$, $\delta Z_1$, $\delta Z_2$, $\delta Z_3$) to three independent ones.