For love of whatever you hold dear, rotate the picture before posting it!

I think you're referring to a loop hoe? It'll work ok to decap the deep root weeds and kill that grass... but like the other person said, it might be in your benefit to spray first. You'll still, obviously, have to rake out the crap after the spray kills off the plants tho. Also, the hoe will knock around those pavers a bit, but you might need to move them to get some of the weeds anyway

I'd probably just buy a cheap sprayer and go with a mix of vinegar, water, and dish soap. You'll have to apply it a few times over the course of 2-3 days but it should kill the grass. Or get some roundup

I just had to do this in some gravel. I used a shovel and and metal rake. Shovel to loosen everything and then rake to get the plants out of the gravel as best as possible. For what it's worth, people are very split on if putting landscaping fabric or tarps down actually does anything good. I know I just redid all my mulch and I didn't bother this time. I did the last two times and things just grew on top of it because dirt will accumulate on top it no matter what you do. Most people in groups that hate grass say cardboard is your best bet.

Shoe and glove for scale!