Q:

Why can Ten-Tails jinchuriki stop the reincarnation of Edo Tensei ninja? 

In one of Naruto's episode, Obito ―after becoming a Ten-Tails' jinchuriki― was able to stop a reincarnated (Edo Tensei) ninja (4th and 2nd Hokage) from recreating its body once it was destroyed. 
What's the special thing that allows a Ten-Tails' jinchuriki to do so? 

A:

It is called Gudoudama or Truth-seeking ball which was gained by Obito after being Ten Tailed Jinchuriki. 

Truth-Seeking Balls are hand-sized orbs of black chakra that users can use to alter its shape to serve for a variety of purposes. 
When one awakens Six Paths Senjutsu, Truth-Seeking Balls appear and float behind their back.  This can be done by becoming the jinchūriki of the Ten-Tails or by entering Six Paths Sage Mode. 

And stated in its usage

Truth-Seeking Balls are composed of all five basic natures, in a way similar to yet surpassing kekkei genkai and kekkei touta.  If imbued with Yin–Yang Release, they can be used to neutralise ninjutsu and by extension become impervious to it; this negates the regenerative qualities of the Impure World Reincarnation, making it possible to kill or permanently damage those who have been reincarnated.