"The tourist is looking for his passport in the backpack."
Translation:Turysta szuka paszportu w plecaku.
Yes, in general Polish language uses possessives much rarer than English language and usually only specify possession when it differs from what would be naturally implied(so, for example: "Turysta szuka paszportu swojej żony w plecaku dzieci", because neither belong to him, but otherwise possessives would be usually dropped by Polish speakers).
Unfortunately it's hard to put the borders sometimes. In a sentence like this, it seems definitely most probable that it is his passport and his backpack, although we accept 'the/a/his/her/their' for English version and 'mojego/swojego/nothing' for both the passport and the backpack.
I found in the course the sentence "Where is my backpack", so assuming this is the one you mean - this is so clearly "my backpack" that we can't omit it, because otherwise the sentence could just mean that you're looking for some backpack in a supermarket...
Woooops! Yeah, the starred-until-now version "Turystka szuka paszportu w plecaku" is wrong, because it implies it's her own passport, and that does not work as the English sentence had "his". Deleted, thanks.
However, there is a version that technically works: "[Ta/] turystka szuka jego paszportu w [tym/] plecaku." -> So the female tourist (Anna) is looking for 'his' (Adam's) passport in the backpack. That one's still possible, especially that 'jego' already says that the passport does not belong to the subject of the sentence. Even if the subject was masculine (Turysta).