Is it redundant to say iterate over? I cannot think of any other word that you'd use with iterate, so is it acceptable (or correct, even) to drop the over?
Iterate over what? I guess that is the point.
To 'iterate' is to repeat something, say, an action, so we can iterate a procedure, or we can iterate over x, or iterate through x. So:
We iterate over numbers one to ten.
We iterate through each entry.
We iterate the above procedure.
The above procedure is iterative.
Note the difference between iterate and reiterate as some might find it subtle, where reiterated becomes continuous:
To say or perform again; repeat.
To say or do again or repeatedly.
In this case:
We reiterate the above procedure until we get a satisfying result.
Iterate is a transitive verb, meaning to repeat something, which is often used mathematically: if you want to say you do a procedure again, you would say
We iterate the procedure.
In mathematics or computing, if you want to say you do the procedure on every object in some set $S$, you would say
We iterate the procedure over the set $S$.
If the person you're talking to knows what the procedure is, you can drop it from the sentence:
We iterate over the set $S$.
You need the word over in this sentence, because you're not iterating the set; you're iterating the procedure.
If you're not talking about mathematics, I don't think you'd use the preposition over:
We will iterate the decontamination procedure for every house in the town.
or, if your audience understands you're talking about decontamination:
We will iterate for every house in the town.