Basically me and my SO circumstances for meeting, which are that we in hindsight were basically in the same grade and had met in person, and her parents found out that wasn't true and now she's grounded for months and her mother (who is the boss, don't have a problem with that) is upset at both of us and is weary of us seeing each other again because we lied about it.

It's a petty story, but regaining the moms trust is important so that we can see other again. How should I go about talking to her mom and apologizing to her about this?