You can change the values of Smart Checklist via Jira REST API by accessing "com.railsware.SmartChecklist.checklist" Issue property,
Refer to Rest API documentation https://developer.atlassian.com/cloud/jira/platform/rest/v2/#api-rest-api-2-issue-issueIdOrKey-properties-propertyKey-put
Cloud
Get your API token from https://id.atlassian.com/manage/api-tokens check out instructions: https://confluence.atlassian.com/cloud/api-tokens-938839638.html
Then use the following approach
curl --request PUT \ --url '/rest/api/2/issue/{issueIdOrKey}/properties/com.railsware.SmartChecklist.checklist' \ --header 'Authorization: Bearer ' \ --header 'Accept: application/json' \ --header 'Content-Type: application/json' \ --data '{"- ToDo List\n+ Checked\nx Skipped\n~ In Progress\n"}'
Check an example implementation with ScriptRunner for Jira (Cloud)
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