Anas Al Borno was lying on a flimsy mattress with his wife and children in a Rafah refugee camp in January when a relative texted with a rare piece of good news. For the first time since Oct. 7, Al Borno and his family were eligible to cross into Egypt.

The main travel agency that arranges such crossings had changed its rules, allowing Palestinians without foreign passports through the land border. But there was a catch — the price to get out for Al Borno and his family was at least…