I'm using Irssi nested in Byobu. Since Irssi has an inbuilt clock, the Irssi window gets marked for activity every time a minute rolls over. Byobu has its own clock, so the feature is not useful to me.
How can I remove it?
You can use /statusbar window remove time to remove it.
You can also use /statusbar window reset to reset the statusbar.
see also
http://irssi.org/beginner/#c12
To add to the other answers: If you want to permanently remove the clock, edit ~/.irssi/config. Navigate its hierarchy:
statusbar = { line.default = {; it will most likely be indented two spaces and situated after the block starting with items = {.default = { block, find items = {.time = { };. Comment that line out or delete it.