I'm confused. Are the two circuits shown in the first photo supposed to be the same? They're NOT!
Figure 238 shows pins 1,2 and 3 all tied together but in figure 239 they are the output, - input and input respectively.
The device that you show in the second photo (you don't show it's part number) may be nothing more than a current transformer and MAY not contain any active circuits. Without a part number and a complete description it's impossible to tell.
In the circuit in figure 238, the line being monitored appears to attach directly to 6 pins in the device but the part in the second photo the insulated line being monitored simply passes thru the the device and doesn't connect to it electrically.
You're not even comparing apples and oranges, this is more like Apples, rabbits and tennis balls! Except for the fact that they monitor current, none of these circuits have much in common.
C77 is there to dampen the feedback of the op amp. It's a common technique, look it up. Get the data sheet for the part it should tell you how to calculate the cut off frequency, but be aware that the cut off will be gradual and not abrupt. These simple one pole RC filters are only intended to block high frequency noise that is orders of magnitudes higher in frequency than the expected signal.