"du" = contraction of preposition "de" (of) and definite article "le" (the).
The trick is that not all "du" match the English "of the".
- the animal of the zoo = l'animal du zoo
- the bottom of the glass = le fond du verre
- he talks about the weather = il parle du temps
- there is still some milk in the bottle = il y a encore du lait dans la bouteille
- he is pouring sand = il verse du sable
"The zoo animal" is an example of the attributive noun + noun construction in which "zoo" modifies "animal".
I think that the French phrase "l'animal du zoo" refers to a specific animal of the zoo (zoo animal), but does not express a generality.
In contrast, depending upon the context, the term "la pollution" can refer to specific pollution (the pollution) or to pollution generally (pollution without article).
The back translation for "the zoo animal" would be "l'animal de zoo", which would refer to an animal living in a zoo, as opposed to one living in a circus or a wild animal living in its natural environment.
Therefore "l'animal du zoo" can only be one thing: a possessive case = the animal belonging to the zoo.
I had no idea what this phrase was intended to convey! I have flagged it up Sitesurf's entry with a lingot. To précis:- "l'animal du zoo"
Here, du is possessive,- the animal belonging to the zoo
It is the difference between the zoo animal,- see above, (e.g. as opposed to one living in a park) and the zoo's animal (possessive apostrophe).
Btw, I should point out that respecting the wellbeing of our fellow creatures is not only our duty but is very much to our mutual benefit.