Scott,

Cut 'em off, with a sterile blade. Clearly, they are done blooming. When a
Phal spike loses its flowers there are 3 things you can do initially. You
can leave it there, cut it off, or cut down at the third or fourth node and
try to force a new off shoot. At this point, though, since the plant has
put out a new spike, it's a bit late in the game for that. Just as well; I
don't often try to force things. Lots of stress for the plant, and it needs
rest now and then.

Hope this helps.

Diana