If you carefully un-bend the crimped edge of the aluminum shell all the way around so the plastic rear plate can pull out, you can service the parts inside. Here are some nice pictures of the parts inside of the manual pump. Photos are compliments of David at www.doanfamily.net.

Gently pry back the flange of the aluminum cannister to open it. Find the rubber diaphragm and a screen inside. The last two pictures show the outlet check valve parts.