Equivalent of phrase 'emu parade' in other English-speaking places
Solution 1:
One phrase is combing an area, from the verb to comb (Merriam-Webster):
3a : to eliminate (as with a comb) by a thorough going-over
b : to search or examine systematically // police are combing the city
This produces a lot of related terms and phrases. For example, beachcombers are people who comb the beaches looking for specific items, such as shells, dead birds, or buried treasure (example: the US Fish and Wildlife Service encourages people to comb beaches for dead mammals and birds). One can also comb parks, rooms, and other areas.
The figurative language has also been made fun of, like in this Spaceballs clip (YouTube) where troopers comb the desert looking for the heroes.
Solution 2:
In AmE, we have the FOD Walk:
foreign object damage (redirected from FOD Walk) TFD
Rags, pieces of paper, line, articles of clothing, nuts, bolts, or tools that, when misplaced or caught by air currents normally found around aircraft operations (jet blast, rotor or prop wash, engine intake), cause damage to aircraft systems or weapons or injury to personnel. Also called FOD.
In a fod walk, people systematically police an area for rubbish (BrE) and clear it of such.
Solution 3:
Not completely equivalent as there is no specificity for objects being sought, but there's beachcombing: searching along a shore for objects for resale.
Similarly, mudlarking, used in the context of scavenging along a river (e.g. the Thames).