Certain foods, including walnuts, can interfere with the absorption of Synthroid, as well at other replacement thyroid hormones, such as Levothyroxine, Levoxyl, etc. The recommendation is to separate these foods from the medication by 2-4 hrs. Of course, it would depend on how many walnuts one is eating, but if there's proper separation there shouldn't be any trouble with absorption.
Most medication pamphlets don't have some of these specific cautions on them. When I was taking Levoxyl, it cautioned against "certain foods" but didn't list them all.