When an invitation includes a request to refrain from gift-giving, it usually means that the sender does not want anything except the recipient's presence at the event. The best way to convey that information is by asking friends and family to spread the word among the invited guests.
The request for no gifts should not go on the invitation, because the suggestion may draw attention to bringing gifts rather than discouraging it. The sender should let guests know that the pleasure of their company is what matters to the honoree. But sometimes guests still choose to bring gifts because they feel it is a nice way to share in the occasion.