Block call history in Project Fi? (Nexus 5X)

This is kind of a strange question, but basically I was helping my friend root/rom tonight, but he said he had to call his parents before we started. We are both freshman in college so his parents are still watching over his shoulder and are also paying his phone bill. They noticed a call in his logs after 10:30 from someone they thought he was with, and thus immediately assumed he was sneaking off/doing drugs/whatever, and proceeded to accuse him of sneaking off on speaker phone in front of me.

Basically, what I'd like to set up if I can, is a way to block calls from being recorded in the call log after 10:30? Is this even possible?

Thanks in advance for any help!

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