= Solution
Take a transverse offset $\mathbf b\cdot\mathbf R=0$. Its distance from the source changes only at second order, but the direction of the gravitational force changes at first order:
$$
\mathbf g(\mathbf R+\mathbf b)
=-\frac{GM}{R^3}(\mathbf R+\mathbf b)+O(GMb^2/R^4)
$$
in its first-order vector expansion. Subtracting the reference acceleration gives
$$
\boxed{\mathbf T(\mathbf b)\simeq-\frac{GM}{R^3}\mathbf b.}
$$
It compresses the transverse separation. Together with the radial result, this is <point-mass tidal stretching and squeezing>, with tensor eigenvalues $(2,-1,-1)GM/R^3$.
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