the cosmonauts gave it a shove in the direction of Earth, in the expectation it will burn up in the planet's atmosphere
Actually they throw if antispinwards of the ISS, which is sane:
"East (spinward) takes you out, out takes you west, west (antispinward) takes you in, in takes you east, port and starboard bring you back."
I don't know whether that little push was enough to make the package drop sufficiently low. Maybe one should have crossbow catapults.