@Bob Sochacki In case "Escalate" button on portal is displayed because it is a transition in your JIRA Service Desk workflow, then you can hide this button/transition from JSD portal by editing your workflow and unchecking "Show transition in the customer portal" option for this transition. And don't forget to publish the updated workflow.
See this documentation for more information : https://confluence.atlassian.com/jirakb/how-to-add-the-escalate-this-issue-link-to-a-service-desk-request-872136162.html
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