To ditch the watermark on videos you've already downloaded, tools like iMyFone MarkGo (Windows or macOS), RemoveLogoNow (Windows), Video Eraser (iOS), or Apowersoft Online Video Watermark Remover (on the web) can do the job.
But what's the fix? Get Rid of the Watermark
Especially if it's your video in the first place, and you plan to re-post it to other services, to maximize reach without duplicating effort. The downside is that not everyone wants the watermark. The upside for the content creator is that the TikTok logo watermark, complete with the creator's name, equals instant branding. You can't do this at all on the desktop via, but you could always do a video screen capture-complete with the watermark, which lasts the length of the video and moves around. Downloading a video on the TikTok iOS app (Note: this only works if the creator marks the video as 'Public.' If it's listed as 'Private,' you won't see the save option.) The video is placed in your phone's camera roll, and you'll see options to share the video from there to SMS, Facebook, WhatsApp, or other services. Hold down a finger on the video, and in the menu that pops up, tap Save Video at the top. This is the easiest way to download a TikTok video, because you can instantly do it on your mobile device, right from within the TikTok app.