Currently no way to see which Climb Portal routes you have completed, other than checking STRAVA. Would be great if you could see them within the Companion App like you can with all other routes. This could include a sub section for the % difficulty you have completed each climb at, maybe even a route badge once you have completed every climb at each % elevation.
Everyone (majority) likes a route badge 
Your suggestion is a good one. Until Zwift make a change one way you can see which Climb Portal routes you have done is to search your ‘Activities’ tab on your ZwiftPower account for Climb Portal. Ensure you save your ride activities with consistent useful searchable words and you can easily find almost any ride history you want.
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I’ll give it a go, thank you.
I just ride them all.
I love the short ones
Looks like the next 3 are long, Stelvio and Fiji.