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Pull the cable out as much as you can, if the cable is covered by a black Teflon coating then don't oil it.
Matt, have you removed the clutch actuator components and given them a good scrub and re grease?
Its not Honda cos the bag its in would look different and have a red and white lable with the Honda name and part number, im not saying it isnt identical to a genuine one just that it isnt.Honda ones also tend to have numbers along the outer, but necessarily the part number
If it's genuine it should be coated, I suspect that's a cheap copy made to a price not to a quality, as such most likely no Teflon. However do the mechanism first to see if that improves it, if oiling try silicon oil not mineral as it's less likely to react with any Teflon if it's there but hidden.