The problem with "rabbit ear" antennas is that they are, essentially, a gross oversimplification to the problem of over-the-air reception of television signals. Assuming your grandmother also lives in Ossining, she is more than 20 miles from the Empire State Building, where the NYC TV stations transmit from after the WTC was destroyed. The signal path between the ESB and Ossining is one of the most hostile to satisfactory TV reception, consisting of large steel-frame buildings and some hilly terrain.

TV signals are horizontally polarized...that is, the RF waves are transmitted in a plane parallel to the earth's surface. Rabbit ears are vertically polarized, so they won't receive enough of the horizontally polarized signal. At those frequencies, reception is via line-of-sight...that is, there must be a direct path (no bounces off of other objects) between the transmitting and receiving antennas for best results. Ghosting occurs when two or more instances of the same signal are received: the line-of-sight signal and others which bounce off of another object and arrive at the receiving antenna a fraction of a second later. If the signals are almost the same in signal strength, the TV set won't be able to tell them apart and will reproduce all of them. The radio waves that produce ghosting can bounce off of virtually any object...even airplanes in flight. If the line-of-sight signal is much stronger, it will override a "ghost" signal, but normally that only occurs within a few miles of the transmitting antenna.

I seriously doubt that your grandmother is going to be satisfied with rabbit ear reception so far from the transmitting antenna. But, they're so cheap these days that it might be worth a shot anyhow. You have very little to lose for trying, and who knows: her place might be in a "sweet spot" where there's little or no ghosting.