Most simply, no you don’t. It is perfectly okay to consider the gift a sign that the person wishes the two of you well. If you are worried they are expecting an invitation, review the possibility with a guest who is close to them. They may know better what information has gone out to that circle of people about your guest list limitations. It will also give you an idea on whether or not adding this one person will mean you have to invite 10 others. If you do decide to add them to the guest list, make sure their invite goes out right away if they have already been sent.