A good earner in removing it and replanting the area with a more easily maintained selection of feature plants.
Removal is probably the way to go. I find it is impossible to keep these features (especially when they have been 'let go') presentable with low price, short time, infrequent visits (and glypho is out of the question for weed control).
It will be shallow rooted - 3 or 4 tyne fork and a metal rake should deal with most of it reasonably quickly. I suggest you glypho spray it first and remove/clean it up after die off a few weeks later.
The larger clumps may be a little deeper rooted but ball rooted - lift out by applying a crowbar plunged through the centre and levering from the inside out, a North, East, South, West (3 ,6, 9, 12 o'clock) pattern is usually enough. (in soft sandy loam soil they may just lift with a shovel)
I make note of the river cobble/pebbles in the picture so jab a crowbar into the ground all over the area before you make any decisions to make sure you are not dealing with any overgrown river pebble areas.
…my just guess on what it is or could be
(a quick visit to the stock yards or websites of your local landscaper supply nurseries will be the quickest way to narrow it down)
more than likely a low/no mow Zoysia var. e.g. https://theplanthub....hp?ref=bluedale or similar low mow type.
hard to tell from just a photo and remember a location, area or region should be included with this type of post as that is always a help.