Your instinct about the seeds is exactly right
A kitten can eat apple flesh in small pieces, and removing the seeds, as your question suggests, is the key safety step. Apple seeds contain compounds that are harmful when chewed and eaten in quantity, and while one stray seed is unlikely to define an emergency, seeds have no place in a pet's food at all. The firm core and stem belong in the same category: out of reach, in the bin.
What remains, the crisp flesh, is a safe occasional taste. Wash the apple, cut away from the core, and serve a thin slice or a few small cubes sized for her mouth.
Why apple stays a taste rather than a snack habit
Apple flesh brings water, a little fibre, and a clean crunch, but it also brings fruit sugar, and a kitten's nutritional priorities lie firmly with animal protein. Cats cannot taste sweetness, so the pleasure she takes in apple is about texture, moisture, and scent, none of which require a large serving to deliver.
A couple of small cubes satisfy curiosity without filling a walnut-sized stomach with fruit. Bigger servings tend to announce themselves later as loose stool, and dried apple, apple cooked in butter and sugar, and apple-flavoured people snacks are different foods entirely, none of them suitable to share.
Cutting apple so a kitten can eat it safely
Wash the fruit well, since kittens mouth the peel if you leave it on, and consider peeling the first serving if you want the softest possible texture for a very young kitten. Slice the flesh away from the core in clean cuts, then inspect each piece once more for any seed that clung to the flesh near the core cavity.
Cut pieces small and thin. A kitten should never be handed a large wedge to wrestle with, both because firm chunks can be gagged on and because a carried-off wedge usually ends with her chewing toward the core you meant to keep from her. Serve the pieces in her bowl or from your hand, and remove uneaten fruit after a short while rather than leaving it to brown on the floor. A piece dropped and batted under furniture is also worth retrieving, since forgotten fruit turns sticky and unappealing long before she rediscovers it.
After the first apple taste
Kittens who try seed-free apple in small pieces typically show no reaction at all, or show you plainly that fruit does not interest them, which is a perfectly good outcome. If her stool softens after a small serving, shrink future portions or drop apple from her list without concern, since nothing in it is necessary to her diet.
If she ever gets hold of the core itself, pips and all, watch her for gagging or difficulty swallowing a fibrous chunk and contact your veterinarian for guidance, sooner if she is coughing, drooling, or distressed. Prevention is easier than the alternative: cores go directly into a closed bin, never onto a plate left on the counter.
Putting that household rule in writing inside KinsLe, under Care Teams, keeps apple prep consistent, so every person who slices fruit for her knows seeds and core never reach her bowl.