A sell-out crowd paid from 880 Hong Kong dollars to see the eight-time Ballon d'Or winner in action on February 4 in an Inter Miami tour match against a Hong Kong select XI.
But the Argentine remained glued to the bench with an injury, drawing boos from the crowd - and then a furore in China, which saw his absence as a political snub.
Organiser Tatler Asia on Monday offered a 50-percent refund for "those who purchased tickets through official channels for the match".
Those who want some of their money back will have to agree to terms and conditions that include not pursuing "proceedings before any court of law, tribunal (or) regulatory authority".
Under fire for its handling of the fiasco, Tatler withdrew its application for a HK$16 million government grant to fund the event the day after the match.
Inter Miami's next stop after Hong Kong was Japan - where Messi played 30 minutes of a friendly match against Vissel Kobe in Tokyo, much to the anger of Chinese fans.
