Should I send Christmas gift?

girlfriend recently ended things. And completely blocked me. Well I emailed and *67 called. Had to get stuff back and wanted to end it civilly. Well she called the police on me. I never once showed up at her house or work. All calls and emails. Maybe 8 times. So... on OkCupid. Meet to hit block but swiped. So I panicked. Called and sent a email. didn't want her calling the police. Explained it was an accident. She called the police! We've had a rocky last month but never like this. Usually make up after a few days. Would like to send an Christmas card, gift and a thank you goodbye letter. I know it's over... do still have feelings. Our last conversation she said she was back on a dating app but also said she was taking time to get herself back, told me it's my fault and goodbye. I'm not sure what to think. How she doesn't really have friends, at times how she talks about my daughter and how I should respond to my ex-wife. Also always wants to be together. So should I just walk away or send Christmas gift and letter? Its been 2 weeks since the okcupid incident.
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