Please note that Chukkung Ri is commonly spelled as 'Chukhung Ri' (or "Chhukung Ri"),
and Kala Pataar is commonly spelled as 'Kala Patthar'.
I was very surprised to see this peak listed at http://www.nepalmountaineering.org/nma_peaks.php
So officially a fee is required, but realistically nobody cares.
The Maoist plague is meanwhile gone. It is actually safer to take the (longer, but very pleasant) Jiri approach because this avoids the risky airplane landing in Lukla.