Change your webcam output to 3 fps, mumble something about a bad connection, and Bob's your uncle.
But more fundamentally:
If I am deepfaking my appearance on video call, I have full control of my machine. I thus can (with negligible lag) just grab the screen content. Once I have that, it's really not too much work to write a filter projecting this screen onto the deepfake image.
In other words: as a 'security by obscurity' method this might have worked for a while, with this now being public knowledge, I expect deepfake software to defeat this within the year, as this really is not a computationally or architecturally demanding change. It is ultimately just a filter, corresponding to screen content, mirrored and super-blurred. That shouldn't have any discernible lag with a modern computer.