Apparatus and related methods for a container lid include a pull structure affixed to at least one end of a tamper evident tearstrip and positioned in an outer flange of the lid, the pull structure having a portion shaped to receive and engage a manipulator such as at least one finger of a user's hand, to assist the user to initiate tearing of the tearstrip from the lid. The shaped portion of the pull structure is configured to eliminate the need to grip the tearstrip between opposing digits of the user's hand. The lid may further include an extendible connection member positioned on at least one end of the tearstrip in an area or space generally defined as a "well." Among other things, the extendible connection member can provide additional flex to a hinge portion of the lid, without destroying the subsequent tamper-evidencing value of the lid. A satellite ring may be attached to or provided on the lid or container to provide further tamper evidencing and protection to the lid assembly.