Might be worth trying a water based acrylic varnish. No real volatiles to off-gas but it does have an odour until dry. Once dry seems to be odour free. Two coats should adequately seal MDF or chipboard. I have used plenty on various projects possibly not quite as hard wearing as a polyurethane product but under a worktop should not be a problem.

I find that many printed items seem to give off unpleasant fumes. Many of the circulars that drop through the letter box are consigned directly to the re-cycling bin outside for this reason.

John

Unless the worktop is something special it is probably chipboard bonded with melamine formaldehyde binder, similar resins are used to bond the decorative paper to the sides Most of the outgassing is from the core. Usually when kitchens are put together the ends of the laminate are sealed either with silicone or an iron on or glued type sheet. Formaldehyde is a small molecule and escapes easily. If your brother has access to a air filter (room pollen filter type devices” with an activated carbon filter running this might help but there is so much else going on in a kitchen is might saturate fairly quickly but might help identify the problem,  else that the laminate “weetabix”s, it could also harbour mould. Check for other leaks that could case hidden mould.