Fiona was friends with the student's aunt. She soft-pedaled because of that connection and didn't fail the student.

I want to say a teacher went soft on her student in terms of handing out a mark. Can I use "soft pedal"? Is this correct and natural?

Fiona was friends with the student's aunt. She soft-pedaled because of that connection and didn't fail the student.

If that doesn't work, what idiom can I use?

'Go easy on (someone)'?

I already knew that. I'm asking about soft pedal now.

The verb 'soft-pedal' means 'diminish or downplay the importance or impact of something' and requires an object to follow it.

To "soft-pedal" is to downplay or deemphasize something.
"Being lenient" would work.