Plants are very different from animals, especially in terms of how they reproduce. Typically we think of a plant growing from a fertilized seed; however, some plants can also be propagated (made to grow) through cuttings (i.e. taking some part of the plant and replanting it directly into the ground!).

Genetically modified seedless grapes are easy to imagine; a scientist knows which genes to alter to prevent the plant from making seeds, and propagates it through cuttings, essentially making clones of the original plant.

However, we know that seedless varieties of certain fruits existed long before genetic modification was possible! It's a much rarer phenomenon, but all organisms have a low level of random mutations, some of which can lead to interesting phenotypes like a lack of seeds. Mutant plants lacking seeds obviously can't reproduce on their own, but our ancestors must have discovered these mutants and propagated them using the same technique.

In other words, generating a fruit or vegetable with a very specific desired trait without genetic modification takes a lot of time and luck!

That depends on what you call "genetic modification".

Seedless grapes are mutants - they were created when something altered the grapes' DNA to cause them not to produce seeds. The cause of this mutation was probably natural; it may have been ultraviolet light from the sun, a naturally-occurring poison in the soil, or just an error in the cells' proteins in copying their DNA. Whatever the cause, human growers saw this, and then began cultivating the seedless grapes. This is called "artificial selection".

Humans have been doing this for many thousands of years, and is how all of our domesticated animals and plants (including grapes) became domesticated.

Technically, artificial selection depends on genetic modification, but it can make do with natural genetic modifications like mutations. The fear of genetic modification that causes it to be banned from organic food is a fear of artificial genetic modification, i.e. intentional mutants, instead of naturally-occurring mutants. Organic growers can (and, indeed, must) use mutants that have occurred naturally, since natural mutation is the source of all differences between different living things (for example, the difference between you, a human being, and a grape vine, all amounts to about a billion years' worth of natural mutations, filtered by the gauntlet of natural selection).

Seedless grapes were genetically modified, very very slowly. People selected the grapes with the fewest seeds to grow, for many generations of grapes. Now the seedless grapes are grown from cuttings of the grape vine that are planted and grow roots. It's not called 'genetic modification,' because it happened so slowly and so long ago.

Here's an article:
seedless grapes

This is a very interesting question because it begs the question, “what exactly is genetic modification”.

Currently, when we talk about genetic modification we typically mean adding or removing a gene from an organism. This could definitely be used to create seedless grapes: just remove the gene or genes responsible for seed creation and you would have seedless grapes. But humans have been creating seedless fruits for much longer than gene altering technologies like CRISPER have been around. By specifically breeding plants that have small seeds together, you can create a new generation of plants that all have small seeds. From there you pick the offspring plants with the smallest seeds and breed them together. If you continue this trend for multiple generations eventually the seeds won’t grow at all. You’ve created seedless grapes!

You haven’t gone directly into the genome and removed the gene or genes for seeds but, in a sense, you have modified the genetics of the grapes. You’ve artificially selected certain traits and designed an ideal grape. But don’t worry, humans have been doing this for years whether it’s creating sweeter fruits or selecting for dog breeds. The selective breeding process is humanity’s first attempt at “genetic modification” and it has occurred long before we even understood what we were doing. Thank you for the question!