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Hello. I'll be happy to assist you.
The short answer is that you MAY be responsible, but I tend to lean that you are not. An invitee, such as a delivery person, is someone who is invited onto the property of another. This invitation usually implies that the property owner/possessor has taken reasonable steps to assure the safety of the premises. The question here is whether you took "reasonable" measures to ensure the safety of people on your property. In this case, there are a couple of things in your favor. First off, you are held to a lower standard when it is something you were unaware of, like a nail in your yard (unless you knew there were nails in your yard). Second, you would not ordinarily expect a delivery person to walk across the yard when there is a suitable sidewalk and paved path to your door.
I wish I could tell you that his claim is baseless, but it is a bit closer call than you might expect it to be. My suggestion is that you contact your homeowner's insurance and let them know, but I think you will likely not be liable.
I hope that answers your question. If not, feel free to ask follow up questions. If so, please remember to "Rate" my answer before you go. Good luck.