Xehanort is surprisingly accepting of her explanation, nodding thoughtfully and forgiving her fairly quickly. It surprises her, but he'd always considered her to be skittish so hearing that she'd had a previous bad experience with someone like him does not come as a surprise to him.
It's Eraqus who is the problem.
His eyes on her are sharp and unforgiving.
In hindsight, that is what made Xehanort forgive her so quickly. He wanted to placate Eraqus. Eraqus who remains mistrustful of her intentions for some months yet, acceptance slow to come.
Nora makes excuses again, this time because her presence makes the usually friendly boy much sharper than normal. She knows that it's him who is the heart of the friend group and doesn't want to sow unease.
It takes a whispered confrontation and a more heartfelt reasoning form Norna - still not the full truth - (plus some nudging from Xehanort) before things calm down.
Needless to say, everyone else is happy about it.
Norna still doesn't intrude on their class, but now she no longer avoids it.