Any of the text in Cobrowse can be customized. The same system which allows you to provide localization for different languages can also be used to adjust the copy in any of the Cobrowse elements.
The available text elements are described in text elements
<script type="text/javascript" >
window.Cobrowse.modal.commandQueue.push(async () => {
const enLocaleData = {
SCOPE_EXPLANATION: "A co-browse session shares only this website with an Example.com customer service agent",
};
window.Cobrowse.modal.addL18nLocale(["en","en-us"], enLocaleData)
})
</script>