I don't think either CLR or vinegar are strong enough acids to have much effect on barnacles. There are products designed to dissolve growth in marine plumbing
systems. Take a look at Barnacle Buster by Trac Ecological. Of course if you are brave, good old muriatic acid should do it.
A safe, non-toxic and biodegradable marine
growth remover. Specifically formulated to meet an industry wide need for a fast, safe, and cost effective alternative to mechanical cleaning
. Can safely be recirculated through sea water cooling
systems, dissolving barnacles, zebra mussels, calcium, rust, lime and all other mineral deposits. Most applications can be completed within 4 hours.
If you decide to go with a strong acid such as muriatic, test it on the basket to see if it will damage the basket. Groco makes strainer baskets out of plastic, Monel or stainless steel
. I don't think it would hurt the plastic but I'm not sure about the metals.