I've never heard of LUK clutches and Googling them I can't find any Honda K20 fitment ones and ff that is the case it's not OEM specification, Honda can charge you for the gearbox work.
To be honest though that's all hearsay and speculation until you confirm with the garage that fit the clutch which one it was. I don't understand why you haven't just gone back to the original garage who fitted the clutch but have involved a third person/garage/specialist?
Also odd as it might sound, K20 clutches don't tend to slip even when they are worn and need replacing, they just get gradually harder and harder to change gear. They will eventually slip when they are completely gone, but by that point you would have had it changed due to gear changing issues anyway.
Always worth checking there is enough fluid in the system.