を Noun modification and use of 条件 - アンデッドアンラック

I’m having a bit of difficulty understanding the third bubble, specifically the 任務 to 条件に part.
What I think I’ve understood so far is:

それに入れると - if you’re able to enter (Union)
任務に尽力する事を条件に - and (if you?) preform missions
追跡から対象外になるんだよ - you’ll be exempt from being chased

This is the first time I’ve seen a noun-modification that ends with just を and also the first time I’ve encountered 条件 in the wild.
条件 is “condition”, so I think it makes sense if the modification of it is the “terms” of the condition. But why is it just marked with に instead with a conditional verb, like 条件を呑んだら? And why is を used here instead of ~する事条件?

I appreciate any help! Thanks!

It means something like “on the condition of” or “on the condition that”.

I think the full expression would be ~を条件にして, but する was dropped. XをYにして is just a pattern where you sometimes drop the して.
So, basically, “Once you join the Union, you’re exempt from being chased as long as (on the condition that) you work on completing your assignments.”

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