For screens without pins or tabs, you simply have to use ingenuity — and a butter knife or flat-head screwdriver as a prying tool. Using the same idea as removing the other screen types, pry up from the bottom or in from one side — at about the center point — getting the tool between the screen and track.
What holds window screen in place?
Spring Plunger
Spring plungers are sometimes called plunger bolts. The metal tab of a spring plunger extends into a groove or hole in the window frame to hold the screen in place.