Neighbor wanting to install privacy screen

[Jacky Johnson]

I'm a new homeowner and recently I chopped down two trees in my backyard. My neighbor on the other side of the backyard suddenly felt they lost their privacy and talked with us about how upset and devastated they are. I installed a privacy screen about 2' x 8' above the fence just to reimburse the neighbors and they said it's not enough. We also discussed that if they were to install another more study and high quality privacy screen and they paid for it, it's ok with me. A few days ago a handyman that I was unaware of rang my doorbell saying that my neighbor wanted to install their version of the privacy screen (2x as tall) and asked for my permission to enter my backyard to complete the installation. I refused the handyman (not sure if he is legit or not). Today I received a letter from my neighbor reminding me of what we discussed and how I refused their handyman and they requested again that they would like to have the handyman come to backyard to complete the privacy screen installation by installing part of it on our side (the neighbor hasn't started installing anything yet). The neighbor also said if I refused by 1/1 of next year, they will start installing it on their side by removing a couple of boards and putting them back in later. Should I let the handyman come in and complete the installation of this privacy screen on my side? What are the pros and cons? (I do not feel my privacy is lost at all, only my neighbor, but I do concern about safety of my home if I allow the handyman to come in). Thank you.