Can I Be Held Liable For My Empty Lot If They Have A Key To Get In?

I went no contact with my parents two years ago, this is their latest escalation to force me to talk to them.

They put a small piece of land, right next to their property in my name when they needed to qualify for a reverse mortgage. It had years of back taxes on it that they expected me to pay.

I took it on and have been paying taxes regularly for the past ten years. It is current on payments.

It has a fence, a lock, and no trespassing signs posted, but they have the key and have been "maintaining" it. They do not ask permission or consult me when they mow or chop down trees, they simply tell me afterwards. Unfortunately.

The property is located in California, I live in another state. But the deed is in my name alone.

I am concerned because they contacted me through my SIL to tell me they want me to sign the property back to them in a trust. I told them no.

They have escalated to strange and intense actions to force me to talk to them, and I think they would absolutely fake or manufacture an injury on my property so they can sue me.

Can I be held liable if they are injured on the property?

Should I change the locks, signs, and have a lawyer send them a letter notifying them to not enter and that I can't be held liable if they do?

Are there any other issues, loopholes, or options I should be considering?

Thank you