Weedkiller for "mind your own business" - bintang

A gardener came up with this curious name for a kind of moss with green leaves, whereas a nurseyman, presented with a specimen, had no idea what it is. It grows up walls but likes hard paths best where it becomes a kind of thick, green coconut matting which is easily to remove in square foot lots. But it is invading my lawn and beds and none of the considerable array of killers from my local garden centre witl kill it, althopugh systemic killers knock it back for a while (obviously not a solutuon on the lawn). Has anyone got any ideas please?

Weedkiller for "mind your own business" - billy25

This the stuff?

tinyurl.com/ycfov4w

Weedkiller for "mind your own business" - bintang

It looks like it, except I have never seen it flower. I will watch it this summer. Many thanks for the lead.