Can you unembroider a company logo from a shirt?

We were issued company shirts – some polo, some oxford, some polyester button-down – to be worn when visiting or Zooming with clients.

At some point in the future, I’ll be retiring and won’t be speaking on behalf of my employer. I see no reason to advertise their company after that point. But some of the shirts are actually pretty comfortable.

Is it possible to unembroider logos from a shirt? Or will doing so damage the shirt beyond wearability?

Broader question: what do you do with company-labelled shirts and sweaters when you no longer work for them?