= Solution
The matter part of the <massless closed-string vertex operator> is
$$
V_\epsilon=\epsilon_{\mu\nu}:\!\partial X^\mu\bar\partial X^\nu e^{ik\cdot X}\!:,
\qquad k^2=0,
\qquad k^\mu\epsilon_{\mu\nu}=\epsilon_{\mu\nu}k^\nu=0.
$$
Its symmetric trace-free polarization is the graviton, while its antisymmetric polarization is the <Kalb–Ramond field>, or B-field. The <mass-shell condition> $k^2=0$ and transversality make $V_\epsilon$ a <primary operator> of <conformal weights> $(1,1)$, as required for an <integrated string vertex operator>.
The graviton polarization has the linearized <gauge redundancy>
$$
\epsilon_{\mu\nu}\sim\epsilon_{\mu\nu}+k_\mu\xi_\nu+k_\nu\xi_\mu,
$$
while the antisymmetric polarization obeys
$$
\epsilon_{\mu\nu}\sim\epsilon_{\mu\nu}+k_\mu\Lambda_\nu-k_\nu\Lambda_\mu.
$$
In either case the change in the integrated vertex is a worldsheet <total derivative>, hence vanishes on a closed worldsheet; in covariant language it is <BRST cohomology>[BRST-exact]. This <string-state gauge redundancy> is the vertex-operator form of linearized target-space diffeomorphism or two-form gauge invariance.
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