My suggestion would be to ask the company to provide you with their crane operator’s license, though if the tree service owns their own crane, legally the operator does not have to have a license to pick trees.
They do have to have insurance (and that’s far more important than the license) and should provide you with proof if you ask. You want to make sure they have General Liability, Worker’s Compensation to cover all workers onsite, and Commercial Auto insurance. The certificate they provide to you also should show your name and address as the Certificate Holder, that will ensure the certificate you receive is current and valid.
As for reach, we work with that same model crane, it’s one of the six sizes we work with here. It will have plenty of capacity to lift your tree as long as the operator and crew know what they are doing. We would most likely be comfortable with that setup, though we may bring a bigger crane just because we can...
I’m assuming the tree is not sitting on the very back of your property, so based on a lifting radius of 80’ from the center of the crane to the center of the tree, that crane will be able to lift 3100 pounds. If the tree is closer, the lifting capacity will increase.