In brief, you should NEVER trust your HDD before handing it over to someone else!

The solution to this would be either wipe the whole HDD or at least wipe the files/folders that you need to keep out of reach.

There are two quick ways to do this on Ubuntu; shred and wipe. I prefer wipe because it can accept folders as well.

The point is to fill the place of your data with random bits multiple times, as follows:

1. sudo apt install wipe
2. wipe -rq folder_name

r: for recursive

q: for quick mode, with only 4 iterations of random data.

Enjoy!

Note: This process is very time-consuming, even in quick mode, depending on how large your data is, and how fast the HDD you are wiping is.

Source: https://askubuntu.com/questions/57572/how-to-delete-files-in-secure-manner