Removing data table columns inside a function

I have the following example:

irisDT <- as.data.table(iris)

mod <- function(dat) {
  dat[, index:=(1:nrow(dat))]
  setkey(dat, index)

  dat <- dat[2:10]

  dat[, index:=NULL]
  invisible()
}

mod(irisDT)
names(irisDT) # it contains index

To my surprise, the index column still exists after the mod() function call . This is not the case when I delete a row dat <- dat[2:10]. I assume that since rows cannot be deleted by reference, another data table is created. However, I would like to remove the index column in the original data.table.