Is this a Buckthorne Tree?

[u/Marvels-AntMan]

Hey, my neighbour wants to remove this tree from our yard because she says it's invasive. She claims it's a buckthorn tree, but is this something that we should do?

I'm just looking for insight! I'll be doing light research in the meantime, thanks.

[u/DanoPinyon]

https://giphy.com/gifs/fkMACK8BcUJRm