Document task table is in "Document templates" application scope. We don't have option to select this scope in background script. For this scope related error you need to create restricted caller access record.
Second way to achieved this is change your scope to "Document templates" and Create fix script. So this fix script will get created in "Document templates" only and then add your code. Then simply click on "Run Fix script".
Also in your code, parent is a reference field so use the HR case sys ID instead of HR case number
var gr = new GlideRecord('sn_doc_task');
gr.addEncodedQuery('number=DOCT0001111);
gr.addQuery('parent','a07f7b8e8a9370cbb354edfdffdfdfdf');
gr.query();
if(gr.next()){
gs.info(gr.number);
gr.setWorkflow(false); //Disable business rules for this query
gr.deleteRecord();
}
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