The pods will length and then open up to reveal the tiny little yellow flowers, and then the fruit, which are dates. I've watched them do this every spring here at The Tropical Paradise and I have to admit that I still really don't know what to do with them. I've made some mistakes so I know what not to do.
• Don't start cutting them off when they appear. No, it wouldn't harm the plant, but it will just make the he whole thing more messy. They will continue to grow whether you cut at them at this stage or not, and will just look worse if you do. My recommendation is to let them grow all of the way out (it will take a few weeks) until you can cleanly cut them off at the base of the stalk.
• Plan on more than two cuts. Like the fronds, the flowers will continue to grow at the base after they are cut. Go back and re-trim them to keep them tidy. I have some very sharp heavy-duty snippers for this. It's just a matter of making it look nice. A pygmy date palm, like this one, looks ratty with long stubs growing out all over the trunk. Trim it up.
But wait until the flowers are finished.