Was it a Haddoni? (green carpet nem doesn't say anything to what it actually is)
I will assume it was.....
When you say flow is not an issue, can you quantify that? Haddoni's do not like much flow. If you are running a full SPS tank with a Haddoni blasted by flow, it's not surprising it took a walk looking for lower flow.
Haddoni's are also a sand-dwelling anemone. It causes me to raise my eyebrows a little to hear it was walking all over your glass. Something wasn't right.
Can you please show a picture of your tank with the anemone? The color "lime green" could really go either way. A good healthy green haddoni could be described as lime green as a way to portray vivid colors, or a bleached out green haddoni could be described as lime green as a way to get across the lightish green tint it has. An image would help clear this up greatly.
You also said light is not an issue. Did you light acclimate the anemone? Haddoni's don't necessarily need the full blasting light that other anemones do. That might cause it to walk around.
Do you have sand in your tank? If not, the nem may have finally gotten fed up with it's situation and went looking for sand.
If you do not have a Haddoni, the above questions may not be quite on point, sorry.
In general, if you ever have an anemone sucked into a powerhead, don't pull it out. It'll usually get itself out. Turn the pump off and let it sit for a long time.