If you need to level them back, you can do that any time with the appropriate equipment for the bed size and the amount of leveling necessary...we'd need photos and more information, like bed size and excess height, to determine that.

Removal of mulch (if any) would be necessary as well.

Planting a new lawn is August. In NH, it depends on where you are and your altitude, and it's about the time that summer just starts to come to a close. For most of us, August 15th. It could be earlier than that for you, but certainly no later, that new lawn planting should start. Before that, though, your old lawn is likely to spread at the edges and begin to invade the beds. I'd just let that happen. :-)

You sort of know the date because it's the first evening you can just whiff the end of summer on the wind. It's not quite so warm any longer. The leaves are a little bronze at the edges. You know what I mean. It gives the seed the end of August to germinate, all of September to grow, and as much of October as they can get to harden off for winter. If some of November is nice enough to grow on, great. If not, it's no loss.

Matthew Siebert, I removed two raised beds when I moved into my house on the north shore of Boston 17 years ago. I just took a shovel and did it. Everything surrounding the beds was weeds. I shoveled the weeds up and piled them into a compost pile somewhere out of sight. Then spread the dirt that I removed from the raised beds into the just created mess. There was no mulch to deal with.

I seeded the area. Things went wrong, so I seeded again. More things went wrong and again I seeded. It took years to figure out what was needed. I now have good grass in most areas. Deciduous trees that drop leaves do damage, both from shade and from rotting leaves that don't get raked up in a timely manner. Good looking grass is hard to grow if you have trees. I am speaking from experience. It can also be difficult in full sun if you are a picky person and want PERFECT grass. I know someone like that, and have followed his progress on his yard.

We should talk grass. In New England, the turf grass that will grow is "cool season" grass. That's because it grows in the two cool seasons, spring and fall. You can seed cool season grass right now, or in the fall, or both if you like. I just seeded two sections of my yard, and will overseed another in a few days. This grass seed will grow until it gets hot, then stop, then start again in the fall.

But you can't put down weed killer at the same time as you put grass seed; it will kill the seedlings. Do you want to kill weeds now and wait all summer to seed the grass? Cool season grass won't grow in the heat. You can eliminate the weeds now with weed killer, wait 6 weeks for the poison to wear off, then seed with an annual grass that will grow in the heat. It will not come up next year because it's annual, but it will look good this summer. Contractors often do this.. Then in the fall you can seed with your permanent choice of cool season grass.

OR... You can shovel up the weeds now (no poison) and seed as soon as you're done with a cool season grass that will be there forever. That will work. It's still cold, so you have time to get rid of weeds if you have them. You can safely seed up till Memorial day.

What's your weed situation right now? That will have an impact on whether you seed just the spot where the raised beds are or everywhere.

There are a number of types of cool-season turf grass that will grow here. The big differences between them have to do with three things: sun needs, traffic tolerance, and growth habit. Some grow in deep shade (sort of, with a lot of TLC), some flourish in full sun (4-6 undiluted hours), others are in between. Some are willing to be walked on repeatedly without complaining; others aren't. And some spread, which is good if you want fast results, but horrid if you don't want the grass reaching into beds of annuals or perennials. You'll need to constantly cut the runners out. Clump grass does not spread.

Let's talk sun first. What's your sun situation? How many trees are there on and immediately around your property? Are they deciduous or evergreen?

Then growth habit and your plans for your yard. Do you anticipate having sections of your yard where you want grass to stop abruptly, on its own, without a significant retaining wall stopping it? Are you willing to put in such retaining structures to stop it from spreading?

Traffic last. Will your family be walking on this grass, playing frisbee or football on it?

Or the expensive and quick solution is remove the raised beds and put in sod where they were. Water every day. Don't buy it from a big box store that sells it cheap. Buy it from a local garden center on the day it's delivered to them. The manager can give you a call. Pay for it over the phone and have it delivered. This way you will know that you are getting live grass, not sod that's been allowed to sit out in the heat unwatered for days. Read up ahead of time on how to keep sod alive; it's tricky, but delivers immediate gratification.