How do you decide if patients who have a multifocal demyelinating polyneuropathy would benefit from surgical treatment of carpal tunnel syndrome?

I would do median nerve ultrasound at the carpal tunnel and see if there is evidence of compression. If so, surgical release is a reasonable option.

I agree with @Dr. First Last that ultrasound may show compression and would strongly point to CTS. For me, the key are the symptoms and signs. Do they have nocturnal paresthesias or when they drive? Do they have a Tinel's sign? CIDP patients do not tend to have classic CTS symptoms.

I recommend an ultrasound/MRI evaluation of the median nerve to distinguish inflammatory from compressive causes. If the ultrasound/MRI demonstrates features consistent with carpal tunnel syndrome, a referral to hand surgery would be appropriate.