Can a TBC fix this distortion?
 

I'm trying to digitise a number of VHS tapes that play on TV without any problems, but when capturing to an Elgato USB capture device results in frame distortion.

This happens periodically throughout the video, not all time time. Sometimes 10 minutes or more is completely fine, then this type of distortion for a few seconds.

Will a TBC like AVT-8710 fix this?

Probably so, yes.

The key here is that it works on a TV, but not capture device. While a capture device can be flawed, this error is unlikely from that, and looks to be skewed due to timing. And the TBC fixes timing.

But make sure it's a good green AVT TBC, not the black one. Otherwise, seek another TBC, like a DataVideo.