How to understand “even to look them over” here?

Question

Why, they had the nerve to question our right even to look them over.

I'm not sure who to look them over.

My thoughts, from the sentence, there are 3 possible subjects for "look them over":

So I get confused about the "look them over" here, could anyone please give me some hints?

"Why, they had the nerve to question our right even 'to just check them out.'" Heh, do you know what "check them out" means :D? I glanced at the source text and it looks like they had been checking out steers for purchasing? So the speaker had been refused the right to check out what he was buying prior to purchasing it. — Teacher KSHuang, Mar 13 '17 at 10:44
@TeacherKSHuang "So the speaker had been refused the right to check out what he was buying prior to purchasing it" So does that sentence have the same meaning of "Why, they had the nerve to question our right of looking them over."? In your opinion, it sounds like "they challenged the speaker's right of looking them over". — Sayakiss, Mar 13 '17 at 11:08
Correct. And it sounds like they not only challenged it, but almost as if they had flat-out refused them. But this is pure conjecture without reading the source more closely. (I had only glanced at it.) — Teacher KSHuang, Mar 13 '17 at 11:09

Tᴚoɯɐuo · Accepted Answer · 2017-03-13 13:49:31Z

Let's say the beach is not private property and we can walk on it, legally:

We have the right to walk on the beach.

The infinitive phrase to walk on the beach complements "the right". It describes the nature of the right.

Here, the infinitive phrase complements "our right":

Our right to walk on the beach is undisputed.

Now let's make "our right" the object:

They questioned our right to walk on the beach.

They said the beach was private. They questioned our right to even look it over.

Very nice example, now I understand it! – Sayakiss Mar 13 '17 at 14:34 — Sayakiss, Mar 13 '17 at 14:34

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