Turkey baster is the correct answer, however if you have shrimp in the tank like peppermints they will steal the food right from the anemone so watch out that they get a share of the mysis as well.
I like to thaw a cube with some tank water, rinse that and place a few drops of Selcon or Zoecon with it to soak in, then add some more tank water and feed the anemonies in my tank.
thomas