How can I get rid of grass growing between pavers in a walkway.

Make a mixture of white vinegar and water add a dab of soap and a dab of salt

Grass will fill in whenever it can, all you can do is get rid of it when it shows up. The only other way would be to dig up entire walkway and put down landscape plastic or fabric. Try vinegar, just be careful to not get it on any plants or grass you want to keep.

The ultimate solution would be to lift them up, and put landscape fabric down, then a layer of sand, and place the pavers.

I had the same problem but then I read about Pickling Vinegar (available at the grocery store). It's stronger than regular table vinegar and works well. I pour some in a dollar-store plant mister then once or twice a week, take my bottle outside and spray any weed I see. Avoid the lawn and flowers. You may see "recipes" that use regular vinegar, salt and soap but just straight Pickling Vinegar will suffice. You need nothing else. Be sure to spray at the start of a hot sunny day as the combination of the vinegar and hot sun burns the weeds.

You could try pouring boiling water between the pavers to kill it. But to be honest it really depends on what kind of grass you're trying to eliminate. Very little will really eliminate grass that spreads by stolen underground. I had to bite the bullet and pull up my pavers, dig up as much of the invasive grass as I could, then lay down a couple of layers of cardboard, then landscape fabric, then dirt and finally my pavers. So far ,so good! Good luck!

I use vinegar and salt in a spray bottle

We use a weed killer to get rid of unwanted grass. Here is the recipe that will kill any plant: 1 gallon white vinegar, 2 cups of Epsom Salts, 1/3 cup Dawn dish soap (blue kind). You can spray or pour it on. Mix well and apply after the dew is gone in the morning. By evening the grass will be dead. If the grass is cut or weed eated back first it makes it easier to kill too. Some of our grass was very thick and had not been cut. We used the weed eater first. It took 2 applications, but it did work. Good luck! This is also not hard on the environment.