There's only one way to get rid of it Batman 2050 - a hands and knees job, making sure you take the root ball out with the plant.
I have in the past been faced with a similar situation ( in my son's garden in NY in fact!), thinking we should wait and see what's growing there already...........but soon realised it was procrastination! Especially at this time of the year, you can see what has grown and you are much better off starting afresh with plants you know and have chosen for your own reasons.
Good luck!

That Grass look like "Creeping Bentgrass" to me, as Anneofiver said Hands & knees job and dig & get the root ball out, Best of Luck as you may find it comes back I'm afraid. :o((

It's a weed grass - might be Yorkshire fog, might be couch, doesn't matter much, needs to be eradicated where its growing,but if its couch, much more difficult to get rid of.

Hi, it looks to me, as if you have both of the grasses mentioned by Bamboo, yorkshire fog is easily identified by the purplish stripes at the base of the tufts, and couch grass by the way the thinwhite roots send out new shoots every few inches, if you leave even the smallest piece of the couch grass root, it will come back, but this is not the same for the yorkshire fog, Derek.

It looks like a type of very thick grass I think they call Buffalo Grass. I saw this growing on lawns in Florida apparently it thrives well there because of the climate.

Thank you all for your reply and suggestions.

I guess I will get my hands dirty and try to pull up as much as I can.

Does any one know how deep I should dig to get the root ball? I am thinking to get it done once so it won't return back soon.

Yorkshire fog is easy,you just dig out the clump with its roots, but couch is another matter - very difficult to eradicate in one, you usually find yourself being vigilant and removing as much of it as you can whenever you see a bit growing.