Connecting a C-wire to a Burnham Independence Boiler
Connect C to the wire-nutted bundle of yellow wires

According to the manual for your unit, the C-wire coming off your transformer is a yellow wire (we know this because the manual has it connected to ground, among other things), that is joined with that green grounding wire and a bunch of other yellow wires, including one to the vent damper plug.  Given that the vent damper connector is likely the plug we see at the bottom of your photos, based on the wire colors going to it, we can then deduce that the junction of yellow wires in your photos is where your C wire should connect to.