Translation:I think that I don't have this permit yet.
Yes, also "dinged" for leaving out "that" - which is non-essential in English. Also, I think we would put the negative in a different place: "I don't think I have this permit yet." It sounds slightly odd to say: "I think such-and-such isn't the case". It's more common to say: "I don't think such-and-such is the case".
I suppose you could argue: "I think I don't have" is subtly different to: "I don't think I have", but the latter sounds more natural.
"Thing" or "think"? The second is correct. I'm not sure about "still" instead of "yet". In English, "I still don't have..." is very similar in meaning to: "I don't yet have...", but I don't know if Duo thinks they're close enough.
Edit: OK, I Googled this for you, because I wasn't sure myself!
"Still" implies that something should have happened by now, but hasn't.
"Yet" could mean that it hasn't happened because it isn't due, well...yet.
пропуска is the genitive of пропуск - but it is also the irregular nominative plural of пропуск. Katzner's dictionary seems to indicate that the irregular plural applies to the definitions of пропуск as "pass, permit, password", but does not note if the plural is different for several other definitions ("admission, admittance, passing through, letting through".)
Also, пропуск has some contradictory meanings. Katzner's dictionary says it means omission, gap, absence, the failure to attend.
It's better to have a natural-sounding translation than one that's overly literal. Languages don't translate neatly, and there's no point in trying to make them do so. Better to find something that is close to the original language as possible while still achieving something natural-sounding in the target language.
I agree this is the more natural English phrase. But in the original Russian, it's the having (the permit) that is negated, NOT the thinking. Saying: "I don't think I have..." is not strictly the same as: "I think I don't have..." In this instance, Duo wants the exact translation, even though it's probably not the way most English speakers would choose to say it.
With due respect to Tina_in_Bristol, Al_Sakharov is also right. Duo's insistence on literal translation is misguided. We read the Russian sentence, we grasp the meaning, and we put it into the appropriate English. Duo should be flexible enough to accept correct renderings that do not follow Russian syntax. We shouldn't have to read Duo's mind in order to come up with an answer that is idiomatically awkward.