You can do that if you don't want anyone to download your TikTok videos. What you should do is:
Go to Profile in the bottom right-hand corner of the TikTok app once it is open.
then click on the 3 dot line
Click on Settings and Privacy.
Select Downloads > Privacy.
Turn the option on or off by tapping on Video downloads.
If you download one of a creator's videos on TikTok or tik tok screenshot, they are not notified.