Edit smart checklists using REST API v3

Does anyone have an example of a put payload that can be used to edit the smart checklist on a jira issue?

When you say “Smart Checklist” do you mean this Atlassian App: https://marketplace.atlassian.com/apps/1216451/smart-checklist-for-jira-enterprise?hosting=cloud&tab=overview ?

If so, then you would have to contact the App Vendor directly so see what their integration options are.