"Edit message” feature for Pump.io is in Beta testing.
Messages with and without attachments can be edited. A User can change both text and an attached image. What is not supported (and will fail on an attempt to send an update): adding an attachment to a message that didn't have one. Or removing an attachment. This is because messages with and without attachments are two different types of objects in Pump.io.
"Edit" context menu item appears, when a Sender is my account and it is successfully verified (i.e. the account can actually post the update).
https://github.com/andstatus/andstatus/issues/221