Baby Tears/Helxine

My garden is overrun with Baby's Tears. Now it's creeping into the lawn. I've been busily digging out what I can. In the flower bed it's completely taken over and it smothers every other plant. I'm carefully working my way through getting it out by using a cement trowel to slide under it and hopefully lift the root mat away.


I've daubed Glysophate here and there and it's burned the places on the lawn where I put it. I don't mind that if it halts the progress of the weed. The Glysophate seems to take a week or two before anything happens?


I've also sprayed it with salt water to see if that helps reduce/eliminate it. I'm sure it'll come back in places and I will have to be rigorous in pulling out when it does otherwise I'll be back to square one in no time


Does anyone have any further advice on how to rid myself of this nuisance weed?