The Extension Housing Bushing
The extension housing is fastened to the tail of a transmission or transfer case. There's a gasket in between the two machined surfaces. If the extension housing has small nicks and burrs on its mounting surface, they can be removed with a file. If it's warped beyond specifications or too severely damaged, replace the housing. Check with the manufacturer's specifications before making a decision. The mounting surface can be checked with a straightedge and a feeler gauge.
The housing contains the output shaft, and most often, the vehicle speed sensor and the extension housing bushing is pressed fit into the housing. Then the extension housing seal is installed to contain the transmission's fluid. The extension housing is sometimes called the tail housing.
A worn extension housing bushing can cause driveshaft vibrations. An inherent lack of lubrication often causes this. A binding u-joint or misalignment causes this accelerated wear. They wear on one side of the bushing. Check for sagging mounts or anything that can cause transmission misalignment. Move the slip yoke up and down; there should be little play. Check the slip yoke for pitting; pitting causes premature wear resulting in a leaking seal.
These bushings may contain an oil hole that must match up with the oil supply passage in the housing. Never deprive a spinning shaft of its lubrication. Bushings brass or soft metal, so they wear before the slip yolk.