A container is provided in the form of a cup-like container body with a round mouth closed by a lid which becomes removably replaceable upon tearing away of a circumferentially extending tear strip which initially surround the mouth rim of the container body as a radially outer, integral part of the lid flange. As the lid is differential pressure-thermoformed, its radially outer region is formed into a generally inverted U-shaped structure which near the juncture of the base and radially outer leg of the inverted U, is provided, within the channel, with an inverted V-shaped notch of substantially diminished wall thickness to provide a line of weakness which preferably extends nearly fully around the circumference of the lid, but for at an angularly short tear-starting site. After the thermoforming step, and preferably in connection with trimming the lid from the surrounding scrap portion of the sheet in which it was formed, a mechanical crimper axially collapses and initially radially outwardly concave annular portion of the radially outer leg of the inverted U, intermediate the vertical extent of that leg, with an upwardly inwardly directed barb or hook which, cooperating with the rim of the cup provides the snap lock feature for securing the lid to the cup. After the initial lidding, it is this barb which prevents removal of the lid until the tear strip is torn away. Other cooperating structures preferably provided on the cup side wall and the radially inner leg of the inverted U provide a surmountable-but-­sufficient snap lock which continues to be useful After the tear strip has been removed. By reference, the desired action of the tear strip in removal is enhanced by simple instructions provided on the container, and/or by provision of a crack-­initiating layer on the inner surface of the lid.