You actually do not need any special apps from the App Store to save media on iOS devices. A simple
TikTok Video Downloader Online tool works directly inside Safari or Chrome on your iPhone. All you need to do is copy the share link from the TikTok app, open your browser, paste the link into the downloader website, and tap the download button. The file will save directly to your downloads folder, from where you can easily export and save it straight to your camera roll in a matter of seconds, completely free of charge.