I find the chlorine rots the string long before my pool thermometer needs cleaning but dealing with lake water, I like the idea of CLR, but I'd try good old soap and warm water first. Just don't use a wire brush since it will destroy the painted numbers.
Depends on what is on the glass and if the numbers are painted.
I might try starting with soakingit in vinegar as away to cut the hard water deposits and it may do some good on algea to kill it. Once dead and dried, it may peel off better than expected.
Being a light acid, I use it alot on things like aquariums to get hard water marks off.