hmmm tried it on my Debian stable with tar 1.14, and did all these things without a problem the File3'Hello.txt was tarred properly, without any errors.
Perhaps you should update your system?
ps. output of tar gave this (used -v to be verbose)
jbrugger@deb:/tmp$ tar -cv -P -T txt.txt -f MyTarFile.tar
File1.jpg
File2.gif
File3'hello.txt
jbrugger@deb:/tmp$

[download]

"We all agree on the necessity of compromise. We just can't agree on when it's necessary to compromise." - Larry Wall.

In reply to Re: TAR Escaping by jbrugger
in thread TAR Escaping by davemcgi

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