moistened and wet are almost close in meaning and they mean
مبلل/مرطب(رطب
مبلل
is read as /muballal/
مرطب
is read as /morattab/ and it is equal in meaning to
رطب
and it is read as /ratb/

Feminine: muballala/mubtalla/rateb - مبللة/مبتلة/رطبة
Masculine: muballal/mubtal/rateb - مبلل/مبتل/رطب

Dear Simon,
The first word that, of course, would come to our minds to meet WET or MOISTENED is (MOBALLAL) like my dear colleagues have suggested, yet as you are researching in the contact points between the Turkish and Arabic cultures, then you need to go back a littel, may be to the first half of the last century, when the first word that would come to minds for WET or MOISTENED was (MUSKKI & MUSKKIA). and here are some examples:
1. When we add some water, liquid, or a syrup to dry a material then it becomes: MUSKKI/MUSKKIA depending on male or female.
A) Watch your steps the garden is wet.
a)إنتبه لخطواتك الحديقة مسقية
B) Have you fill the jars ?
b) هل سقيت القلل
C) Add cold syrup to Konafa just after you get it out of the oven.
c) إسقى الكنافة بالشراب البارد بمجرد إخراجها من الفرن
2. Now that brings us to a famous and traditional meal that used to be known as (TUSKKIA) (تسقية) it's now known as (FATTA), and that's because you add meat soup to rice, toasted bread then flavour it with vinigar and garlic. And I think this is where the two culturs met.

I hope that could help you.

Hatem Fathy