Our washing machine drains into a wash basin. there is a drain filter that keeps getting clogged with lint and

the basin overflows and then i have to wet vac up the mess. my wife seems to be resistant to cleaning the lint out of the drain filter for every load. could i just leave the drain filter out permanently if they only thing being dumped into the basin is washing machine water and dirty water from when i flush the furnace? could either of these things eventually seriously clog the pipes if i leave the filter out?