Perek Shira: How To Get Rid Of The Flies From Your Table
The Isha HaShunamis, whose home Elisha HaNavi
stayed at, commented that despite Elisha's modest nature, she knew
Elisha was a holy man. How? The gemara says (Brachos 10b) that she
saw that there were no flies near his table. The Ben Yehoada explains the in Perek Shira it says that the fly says Shira when Bnei Yisroel is not learning Torah (The Yetzer Hara is compared to a fly). So the Isha HaShunamis concluded that since there were no flies on his table, he must constantly be learning torah.
This is why, says the Ben Yehoada,
flies gravitate towards a table full of food. Since there is a special
obligation to learn torah at the table during the meal, the flies come
to see if the participants are discussing torah by the table. If they aren't,
the fly will have its opportunity to say Shira.
This would also explain the miracle in the Bais HaMikdash that in the place where they Shechted the animals, there were never any flies (Avos 5:5). Although MiDerech HaTeva you would expect the flies to swarm the freshly slaughtered meat since this was a Makom Kadosh of pure Deveikus to Hashem, the flies had no opportunity to say Shira there and therefore stayed away.
So If you are having fly problems, it may be worth adding a little more torah discussion to your table. There is plenty of upside benefit in any event.