It would be virtually impossible to scramble either the image, or how the VCR records on a hardwired setup. Does it ever happen when you're around?
What's a lot more likely, is that 'your girlfriend' is switching the channel it records from (like to channel 0, which only shows snow) when lover boy's coming over. I can hardly believe you fall for it.
My suggestion is for you to get another setup you can put outside the house. Maybe in the garage, with the VCR hidden, or at a neighbors Don't tell your girlfriend about it. While you're waiting for 'the evidence' your best protection would probably be condoms.
Sorry.
I'm loving the answer from the guy under me. He's all into INTERFERENCE and GHz, and totally ignoring the fact that you said it's a hardwire system. Interference my foot.
Later...
I see he read my answer, then added a new first paragraph. Unfortunately, all he did was say the same thing I'd already said. His answer still doesn't explain how loverboy is tampering with your setup. A hardwire setup can only be 'scrambled' by someone TOUCHING IT. You'd have taped him walking up to your house, before the interference started. All the evidence you need 'for the police to step in'. If you're not even able to get a picture of this guy coming into the area, someone (named 'girlfriend') is protecting him.
Sorry again. The very idea that you're gone so far to try to protect your girlfriend, probably mean you really care. I just hate seeing people taken advantage of.
After your additional comment.
If you believe 'the one guy' is right, there isn't much anyone can say that will change it. There are plenty of women who live with, and love, horribly abusive partners. It is also very common for abusive and controlling partners to beg, promise, and plea that their behaviors will change when they feel themselves losing control of their victims. It's also very easy for women to want to believe them, protect them, and not want to see them in jail. Especially when they have children with them.
You only want answers that fit into what you believe. If I were you, I wouldn't even attempt putting up a hidden camera. Probably better to not know.
Best of luck to you and your girlfriend.