"This is between us and them."
Translation:C'est entre nous et elles.
"Ils" is used ecxlusively as the subject of a verb. In this sentence you have to use the stressed pronoun "eux". By the way, the English sentence can be translated two ways : "c'est entre nous et eux" or "c'est entre nous et elles" (elles does not change from subject to other functions)
After a preposition, you need a stressed pronoun.
The stressed pronouns are: moi, toi, lui, elle, nous, vous, eux, elles.
As you can see, some of them are the same as their subject pronoun form, but not all.
Therefore "ils" cannot work after "entre": "entre eux" is correct.
"Leur" is the indirect object form, when the verb is constructed with the preposition "à":
Je parle à X et Y --- Je leur parle.
"Leurs" in plural is the plural possessive adjective translating "their": leurs enfants = their children. When the possession is singular, you use "leur": leur enfant = their child.
The option does exist in the list of translations. But if you get the word tiles to compose a sentence, there is only one variant of translation per set of tiles.
The only way to escape the word bank in those exercises is to use the "keyboard" feature to enter your own translation.