How to extract a compressed TWRP backup? There are a couple questions concerning how to extract a TWRP backup in this community, but none of them is really useful. All I found out is that the files like data.ext4.win000 are the tar archives, and I should be able to extract them via the following commands:

$ cat data.ext4.win??? | tar xvf -
$ cat data.ext4.win??? | tar xzvf -


Yes, that's true, when I type one of the commands above in a terminal, I can see that the process of extracting files has begun. But when it finishes, I can also see this message at the end: `

tar: Exiting with failure status due to previous errors 


Looking through the lines leads me to this:

tar: Malformed extended header: missing equal sign


I can find many of those messages in the tar log, but when I check the size of the extracted dir, I can see this:

$ du -sh data/
1.6G    data

$ ls -hal data.ext4.win???
-rw-r--r-- 1 morfik morfik 929M 2019-01-28 01:48:28 data.ext4.win000
-rw-r--r-- 1 morfik morfik 945M 2019-01-28 01:49:47 data.ext4.win001
-rw-r--r-- 1 morfik morfik 549M 2019-01-28 01:50:23 data.ext4.win002


So it looks like it extracted only the fist tar file. I don't know whether any of the files in the archive was damaged during the process. 

Are there any linux tools that would extract this backup in some easy automated way?
It's not a "paged tar", but each file is a TAR itself.

All you need to do is tar xzf on each file.