There is a hidden Content snippet you can define that tooltip text
simply create a snippet called: Portal/Lookup/Modal/Grid/Search/TooltipText and add your value there
This will apply to every lookup search in the Portals, we can't define (via configuration) it for a specific lookup attribute
you can also define the search placeholder using the following content snippet: Portal/Lookup/Modal/Grid/Search/PlaceholderText


if you need to be specific for a certain Lookup attribute, I would recommend applying JavaScript customization then