/jp/ - Otaku Culture

Does "negative verb + てもいい" carry the nuance of telling someone that they shouldn't do something?

In this page Miura says 「とらなくてよろしい」and by the context it seems like she would be telling Yotsuba that she shouldn't be catching something like frogs, but the only way I've ever seen てもいい used is for permission. The DoJG says that when this grammar is used with negative verbs it just means "it's okay if you don't do [verb]," which doesn't really make sense in this context.

Is the bottom left just 「〜ていい」, but with よろしい instead of いい?