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Gravitons have no mass. So there is no problem of escaping, no anomalies.
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I thought a photon was without mass and yet they do not escape our black hole so saying a graviton is mass less does not solve the anomaly in my view.... so I must still be missing something .
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In GR photons travel along what are known as null geodesics or the shortest pathway that can be taken in a gravitational field.
For black holes, this null geodesic wraps itself around the black hole inside the horizon. The photon isn't held there due to gravity but is constrained by the extreme space time curvature.
Gravitons being massless and not being photons are not constrained by gravity or null geodesics.
If it was a paradox would occur. How could the force of gravity exist between a black hole and an object if a graviton cannot be emitted.
Regards
Steven