The meaning of "clearing products or supplies through customs"
Solution 1:
When your goods are cleared through customs, you are allowed to take them into the country.
This comes up in a discussion of corruption because it is common in some countries for the customs officers to expect bribes before they will clear your goods and allow them to enter their country (where you might want to sell them, for example).
So it is a "giving permission" for the goods to enter a country but it is also a "removing" because it allows you to remove the goods from the customs office and take them somewhere you can make more money on them.