It would've great if you can share the product name. However as you know that Oils are categorised into Non aqueous base solutions. you need to have some surfactant or emusifying agents to lower the viscosity so that oil can pass through the suitable type of membrane.
Just to make it simpler I want to quote few lines from USP "Oils and oily solutions of sufficiently low viscosity may be filtered without dilution through a dry membrane. Viscous oils may be diluted as necessary with a suitable sterile diluent such as isopropyl myristate shown not to have antimicrobial activity in the conditions of the test. Allow the oil to penetrate the membrane by its own weight, and then filter, applying the pressure or suction gradually. Wash the membrane at least three times by filtering through it each time about 100 mL of a suitable sterile solution such as Fluid A (see Diluting and Rinsing Fluids for Membrane Filtration) containing a suitable emulsifying agent at a concentration shown to be appropriate in the Method Suitability Test, for example polysorbate 80 at a concentration of 10 g per L (Fluid K)"
Polysorbate or Tween are commonly used for emulsification but again it all depends upon the nature of product for its adherence capability to membrane or not (eg. Harmonal, Protein etc). This is matter of validation of your method suitable for membrane filtration.
Hope I answer your query..please feel free to discuss if you need further clarity.