= Solution
Using the source's rounded solar mass, each hole has $m\simeq3\times10^{31}\,\mathrm{kg}$. Its <Schwarzschild radius> is
$$
r_s=\frac{2Gm}{c^2}
\simeq\frac{2(6.7\times10^{-11})(3\times10^{31})}{9\times10^{16}}
\simeq4.5\times10^4\,\mathrm m.
$$
Thus $\boxed{r_s\sim10^5\,\mathrm m}$ at order-of-magnitude accuracy. Using the more accurate solar mass would give about $9\times10^4\,\mathrm m$.
\b[The stated orbit is not a consistent separated-hole weak-field binary.] Its nominal center-to-center separation is only $20\,\mathrm{km}$, below even the above single-hole radius. Applying two isolated <Schwarzschild spacetime> descriptions and a circular Newtonian orbit at that separation is not controlled. Likewise an estimate $\bar h'_{11}\sim r_s/r$ at $r=10\,\mathrm{km}$ is of order one or larger, contradicting the small-perturbation assumption. The intended near-source statement is therefore a strong-field scale,
$$
\boxed{|\bar h'_{11}|_{\mathrm{near}}\sim1,}
$$
not a reliable prediction from <linearized gravity> at the specified orbit. The exact radiative component is also gauge dependent near the source.
One can still estimate the intended distant <gravitational wave> strain scale. A radiative amplitude decreases as $1/D$ in the wave zone. A compact strong-field source has a characteristic length of order $r_s$, giving a dimensional strain estimate $h_{\mathrm{far}}\sim r_s/D$, up to mass, orientation and efficiency factors of order unity. This is also the strong-field dimensional scale suggested by <far-zone quadrupole strain>; it is not an application of the slow-motion formula to the inconsistent orbit.
With the supplied conversion,
$$
D=500\times10^6\times10^{16.5}\,\mathrm m
\simeq1.6\times10^{25}\,\mathrm m,
\qquad
h_{\mathrm{far}}\sim\frac{4.5\times10^4}{1.6\times10^{25}}
\sim3\times10^{-21}.
$$
For a ring radius $a=4\times10^3\,\mathrm m$, part (c) gives a single principal semiaxis displacement amplitude
$$
\boxed{
|\delta a|\sim\frac{a h_{\mathrm{far}}}{2}
\sim6\times10^{-18}\,\mathrm m,
\quad\text{of order }10^{-18}\text{--}10^{-17}\,\mathrm m.
}
$$
The difference of the two principal semiaxes has twice this amplitude. This is a conditional dimensional estimate of a physically plausible merger signal at that distance; the supplied close circular orbit does not define a self-consistent waveform or a precise amplitude.
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