Images not changing

I think the problem here is simply that the settings form does not clear the cache.
When the block is built it should declare it's dependency on the block settings.
So in a module hook it can be done like this.

/**
 * Implements hook_block_view_BASE_BLOCK_ID_alter()
 */
function my_module_block_view_bootstrap_simple_carousel_block_alter(array &$build, \Drupal\Core\Block\BlockPluginInterface $block) {
  $build['#cache'] = [
    'tags' => $build['#block']->getCacheTags(),
  ];
}

but better still, in this module's block plugin Drupal\bootstrap_simple_carousel\Plugin\Block\CarouselBlock::build() should just include this:

    $build = [
      '#items' => $this->getCarouselItems(),
      '#settings' => $this->moduleSettings,
      '#theme' => 'bootstrap_simple_carousel_block',
      '#cache' => [
        'tags' => $this->moduleSettings->getCacheTags(),
      ],
    ];

And here's a patch for that

Thanks @matslats, your fix was applied in version 8x-1.65 and will move on new ones.