Meaning of a strange Feynman diagram for the $phi^3$ scalar Field theory

Background

I am considering a scalar field theory with $simphi^3$ interaction term, with Lagrangian
begin{equation}
mathcal{L} = frac{1}{2}left( partial_muphiright)^2 – frac{m^2}{2}phi^2 – frac{eta}{3!}phi^3.tag{1}
end{equation}
In the interaction picture, this gives the `interaction Hamiltonian density’ as
begin{equation}
mathcal{H}_I = frac{eta}{3!}phi^3,tag{2}
end{equation}
which I use to expand the $S$-matrix,
begin{equation}
hat{S} = Tleft[ 1-frac{ieta}{3!}intmathrm{d}^4z;phi(z)^3 +frac{(-i)^2}{2!}left(frac{eta}{3!}right)^2intmathrm{d}^4zmathrm{d}^4w;phi(z)^3phi(w)^3 +ldotsright].tag{3}
end{equation}
I then consider the various contributions to the amplitude $$mathcal{A}=langle q|hat{S}|prangletag{4}$$ using Wick’s theorem. There are no first order (in $eta$) terms.

Question

Omitting prefactors, one of the second-order terms goes as
begin{equation}
mathcal{A}^{(2)}_1 sim langle 0|:hat{a}_qphi(z):|0rangle langle0|:phi(z)phi(z):|0ranglelangle0|:phi(w)phi(w):|0ranglelangle0|:phi(w)hat{a}^dagger_p:|0rangle,tag{5}
end{equation}
where $:ldots:$ denotes a Wick contraction and $a_q/a^dagger_p$ are annihilation/creation operators. This gives an amplitude
begin{equation}
mathcal{A}_1^{(2)} = frac{(-ieta)^2}{8}intmathrm{d}^4zmathrm{d}^4w;e^{iqz}Delta(z-z)Delta(w-w)e^{-ipw},tag{6}
end{equation}
where $Delta(x-y)$ is the Feynman propagator.

What is the meaning of this term? It appears that I have an incoming particle with momentum $p$, which then turns into a bubble and vanishes from existence… likewise a bubble appears from nowhere and turns into a particle with momentum $q$. However, were I to carry out the $z$ integration, for example, would I not have a factor of $delta(q)$? What is the interpretation of these delta functions?