That is not a current canning recipe!! The concentrated sugar will clump up due to the natural pectin that surrunds the clump of sugar. Making a recipe like that is not very good if there are also grape seeds in them. Usually everything is mashed and the juice is extracted from the grapes and brought to a boil while gradually adding sugar and stirring constantly. Reopen the jars and pour the contents back into a big pot, and bring to a boil. If it has seeds, run it through a strainer first. Those clumps will never dissolve as they are encased in solidified pectin.

Not only that, but you may have tartaric acid crystals that will be sharp like glass. They are not unsafe other than they can cut your tounge.
You can turn the jars upside down and shake a bit to see if that helps dissolve the sugar. Guess if you get crystals you can strain them out.
Seems like a strange way to make grape juice since you just canned the whole grapes. I wouldn't call that grape juice.

I opened one to see how hard the sugar was at the bottom. It was fused to the jar!

I ended doing as suggested... I opened them up, strained them, and brought them to a boil again. I added some more sugar since most was fused to the bottom of the old jars. I recanned them in new, sterile jars. A lot of work but the juice came out nice. (Although I may have added a little too much sugar.) Overall the juice is much stronger than I would have guessed.

Thanks for your help!

That was an odd way to do grape juice! In the future, of you want to add liquid, it would be good to add some frozen grape juiice concentrate, which will also increase sweetness and acidity. What kind of grapes were used? As to the clumps of sugar, pour boiling water into each jar and allow it to sit a few minutes, pour it out and refill the jars with boiling water again. Eventually it will loosen and release from the glass jars. If you have something pointed (knife) to push into the solid mass it should allow water to soak in deeper and then the sugar will dissolve a bit more. It may need several rinses and soaks of boiling water to remove it all. Think of it this way, you just made a big massive 'gummy' grape..

My best grape juice is canned similar to bfahnl's. I first place 1/4 cup sugar in each quart jar and add 1 cup boiling water and stir just enough to separate the sugar crystals. Then add 1 cup concord grapes and fill jar with boiling water and HWB for 30 minutes. When removing from the canner, the sugar is totally dissolved. When ready to serve I simply invert the quart jar over a strainer and pitcher. Don't squeeze the grapes and the juice will be clear and ready to drink. Strained volume is 3/4 quart of juice.
The only drawback is needing plenty of quart jars.
I have tried making the concentrate and find it is very messy and time consuming.
Has anyone tried the BBB recipe for canning grape juice? It sounds absolutely ridiculous. Imagine heating 1 cup of water with 1 gallon crushed grapes, putting it through a cheesecloth bag twice and having any volume left to can.
The least they could do is call it grape juice concentrate.
You would need more than a peck of grape to get 1 gallon crushed. It would be quite costly unless you grow you own grapes.

When I was a kid, quite a while ago, my mom made grape juice this way. She used a strainer to strain the grapes and whatever before we drank it. It was very good. She would have to can zillions of jars, there was 4 kids.She never had a problem canning it.

If store bought frozen Welches grape juice concentrate is cheap enough in stores, I go for that instead. I made many a jar of grape jelly using the frozen juice concentrate.

I made this this year. But with only 1/4 cup of sugar. We drank our first jar yesterday. It was yummy. But even with 1/4 cup of sugar, it was a bit too sweet for us. I think I'll go with less sugar or no sugar next year.

I loved the ease and simplicity. The "hardest" part for me was getting 7 quarts of boiling water to fill the jars - in a form that could easily be poured into the jars!