Sugarloaf2, iguanas are herbivores; thus they eat all parts of the plant - leaves, fruits and flowers.
I spent much of my formative years on an island in the Essequibo river - the largest waterway in Guyana. The island abounded with iguanas until they became a table delicacy.
So much so that the island is named 'Leguan' - of Dutch origin and referring to the iguana.
That does not make me an expert on the subject of iguanas; just a collector of trivia.

Iguanas are considered an exotic and invasive species in Florida so you can trap and remove any without any permits, if desired.
Plantings need to be protected with fine mesh screening.

Here is a link that might be useful: Iguanas in Florida