I just bought an anemone the other day and its definately trying to find a place in the tank...Also found this...
Anemones have three very distinct layers that make up their radially symmetrical body plan. The outer ectoderm, inner endoderm and a mesogloea which resides in between the two. The mesenteries are the meat of the anemone, containing filaments that look like spokes of a bicycle wheel and are responsible for providing large surface area for gas exchange, in collaboration with an important site for digestion of food and development of gametes.
These whitish filaments can be released by anemones through the mouth in the middle of the oral disc or column wall. This ability for anemones to release these acontia or mesenterial filaments is often times a direct result of some form of physical duress associated with temperature variances, water flow, salinity changes, or physical disturbances brought upon by such things as poor handling practices.