In the past I've left most of the agar on. A year later when I replanted it was still pretty much there. It depends on the agar... if it comes off easy I take as much off as possible without disturbing the roots. The seedlings definitely do better without too much agar.
I also find that it's better to get the seedlings acclimated to your growing area as soon as possible. The idea is to start watering a little more because there is a relationship between how fast you can grow seedlings and the amount of water you give it. The more you CAN water a seedling the faster it will grow. If they're not drying you can't water.
I generally take about two weeks or so to acclimate seedlings to my growing area.
Also, if you do keep your compots in a ziplock or use domes you should let the seedlings dry off after watering before returning them to the ziplock or covering back up with the dome.