First, a thought experiment: at an event outside a black hole horizon a
wrench, initially at rest in the r-coordinate, slips from our hand and
begins falling towards the hole.

Three possible follow ups:

i) We jump into our pursuit rocket, zip after the falling wrench,
brake, and climb back to our starting radius.

ii) We don't try to catch the dropped object ourselves, but radio ahead
to an observer stationed closer in to be on the lookout. He catches
it, and sends it back to us on the next rocket up.

iii) There possibly isn't even time to send a radio message. However,
as luck would have it, some brave soul almost at the horizon sees our
wrench flying by and catches it, later returning it (possibly to our
distant descendants) after he climbs out.

A definition:

"Retrieval Time of type n": an elapsed time beyond which, for a
particular dropped object, no retrieval (return to sender) is possible
by the numbered retrieval method.

A question:

Have retrieval times of types i,ii and iii been calculated for the
Schwarzschild geometry?