Disconnected scalar three-point tadpole

In a theory with interaction $-g{\phi }^{†}\phi \varphi$, the neutral correlator $⟨T{\phi }^{†}(x)\phi (y)\varphi (z)⟩$ contains a connected three-leg contraction and, unless subtracted, the disconnected product of a free complex-field propagator with the induced one-point function of $\varphi$. At first order the latter is proportional to $-ig{D}_0(x-y)D_0(0)\int d^{4}w{D}_m(z-w)$. Vacuum-bubble normalization alone does not remove it. Normal ordering, a vanishing-tadpole condition, or taking the connected correlator does.