Clarification
The oil extracted from the paste still contains emulsified water, fruit particles and mucilage in suspension. These substances compromise the quality of the oil as much as they promote oxidation, hydrolysis and fermentation. They are removed by processes of clarification. 
 

Yesterday
Traditionally clarification was achieved by sedimentation, allowing the oil to settle for a long time, free of sudden changes in temperature. The sediment was then collected with decanting ladles. The last drops of oil floating on the vegetation water or on the dregs were collected with a broad, flat spoon with a handle, the lecca.
Another method for removing impurities was filtering: oil was channeled through containers that had bottoms fitted with vegetable fibers matts that captured impurities as the oil flowed though them.
Filter, 19th century
The picture shows a Venetian filter that employed hot water; it was poured on the oil to bring foreign matter (twigs, leaves, ecc.) to the surface where it could be easily collected.

Today
Even oil obtained with modern extraction systems, regardless of the one adopted, is still a crude must, turbid and opalescent due to impurities. Generally it is left to decant until the latter have settled. The oil is then channelled to other containers. The most demanding producers filter the newly extracted oil with special cellulose filters that are capable of blocking the tiniest impurities and even microscopic drops of water. 
Filtering through cellulose sheets
The picture shows the filtering operation and purified oil issuing from the filters.