Media gallery images url instead of ID on WP API

Have a look at wp_get_attachment_image_url for getting the URL of images: https://developer.wordpress.org/reference/functions/wp_get_attachment_image_url/

or wp_get_attachment_url for getting the URL for attachments other than images: https://developer.wordpress.org/reference/functions/wp_get_attachment_url/.

These functions return the URLs only and you could use them like so:

// your JSON
$json = '
    {
        "Gallery Images": [
            "1833",
            "1834",
            "1835"
        ]
    }
';

// convert it to PHP array
$array = get_object_vars( json_decode( $json ) );

// loop through array and get the image URLs
foreach ( $array['Gallery Images'] as $id ) {
    $image_url = wp_get_attachment_image_url( $id );
}

You could also retrieve more than just the URL, wp_get_attachment_image_src for example returns width and height of the image file as well: https://developer.wordpress.org/reference/functions/wp_get_attachment_image_src/.