No don't remove it.....it should be in orchid 'compost' which looks like small bark chippings. It depends which variety it is I suppose but I have to disagree with shylock, sorry, about mollycoddling.
I'm not very good with indoor plants, outdoor ones are my thing, but I've had a moth orchid for 5 years
like this. It's on a west facing windowsill, unless it's a very hot summer when it's moved back, watered lightly once a week (if it's lucky) with a couple of drops of plant food in & has always flowered for 5 - 6 months at a time, with a 2 - 3 month rest in between.