If we make the assumption that time travel is actually a possibility and this woman is actually holding a cell phone, we have to admit there was no technical cell phone infrastructure in the 1920′s to carry a cell phone signal!
(i.e. most obvious no cell towers to carry the signal or the CDMA encryption/decription for the signal to work)

The only radio carrier waves available were AM signals in the 1920′s

However, if we restate the caption that the woman is talking on a “walkie talkie”, with another person then it’s technically credible. Since both time travelers would hold the technology to both transmit/receive in their hand held devices. BUT ONLY IF YOU BELIEVE in time travel.

I wasn’t sure if time travel occured in a dimension that would allow use of cell phone towers in another dimension, a sort of parallel universe. Anyway, this is probably going much too far now that Halloween has passed!

Thanks for the comments and the 1924 Siemens hearing aid is a great explanation.