The Medrash (Rabbah 19:15) explains this pasuk by saying that whenever Klal Yisroel is in pain, the Avos also feel pain. That is why the Avos felt pained when we were in Egypt.
We may ask why they told this to Edom?
Sefer Agrah D’Kallah explains that Esav was very proud of the way he performed the mitzvah of Kibud Av. He took great care of Yitzchok and always boasted about this.
With this in mind, when the Jewish people met up with Edom, they told them that if they would harm them, the Avos would feel the pain too. They thought that this would deter them from harming them and that they would allow them to pass by peacefully because they surely wouldn’t want to cause pain to Yitzchok, whom Esav claimed to care about so much.
However, this did not work and the people of Edom still tried to harm the Jews. This was a clear sign that their Kibud Av was not genuine and was only a trick Esav used to make himself look good.