The predominant species on Bonaire is the green iguana "
Iguana Iguana"), identifiable by the (usually) white large, smooth scale on the cheeks which other iguanas don't have. Ana, a number of references do classify them as native to Bonaire, which I assume means they were there before Capt. Don.
And "chicken of the trees" are a reliable, cheap foodsource on the island.
Confusion over their status is understandable. On Grand Cayman, registrants can register to cull green iguanas and are paid $5 for each carcass: The green iguanas have done enormous damage to the populations of native blue and rock iguanas on Grand, and are a real disaster (as they also are in Florida). They hit the millionth culled iguana payment when we were there in early November 2019. On Little Cayman, green iguanas are non-native, and considered so destructive that identification of one on the island amounts to an ecological emergency (here's a semi-puff piece about the fierce and fun woman who is spearheading the effort on Little Cayman,
Champion of the rock iguanas - Cayman Compass). The greens undermine buildings (and, recently in Florida, a dam) and denude trees--and saddest, can do serious damage to bird populations by preying on eggs and nestlings. (Last fall, I watched one outlast a Great Blue Heron on a hummock in Wakodahatchee Wetlands, a wonderful preserve in Delray Beach, and then move in on the eggs.)
We've always enjoyed seeing the green iguanas on Bonaire, and will doubtless do so again when we head down next month. But where they are recent invasives, they can be a huge problem.