Therefore I think Robin is commenting to Nami that she thinks there's bad history between Keimi and the island.
Another aspect that leads me to doubt that Robin is talking about Keimi's own history with the island is the usage of the word "rekishi".
歴史 "rekishi" is generally used for "history" as in "world history" or history going back several generations. It is not used for describing an individual person's history (way too short). Instead, 過去 "kako" ("past") would be used if Robin had been talking about Keimi's own past/history with the island.
And, yeah, my prior thought that Robin was referring to the WG Founders seems off-base the more I think about it. Most likely it's about mermaid oppression or some such.
Oh, and I don't really care how I spell Keimi's name as long as it's close enough in pronunciation, so I just follow whoever I'm quoting.