Hamas gunmen shot Emily and killed her dog when they attacked Kibbutz Kfar Aza almost 14 months ago.
Mandy also hid as Hamas stormed her home and was only saved when one of the bullets jammed the lock of the room she was hiding in.
About 1,200 people were killed that day, while Emily and 250 others were taken back to Gaza as hostages.
The US, Egypt and Qatar have spent months working on a deal to secure the release of the 97 remaining hostages in return for a ceasefire in Gaza. But the negotiations have stalled, with Hamas and Israel blaming each other for the impasse.
Without directly mentioning Hamas or Gaza, Donald Trump wrote on Truth Social on Monday: “Everybody is talking about the hostages who are being held so violently, inhumanely, and against the will of the entire world, in the Middle East - but it’s all talk, and no action!"
"If the hostages are not released prior to January 20, 2025, the date that I proudly assume office as President of the United States, there will be ALL HELL TO PAY in the Middle East, and for those in charge who perpetrated these atrocities against humanity,” he warned.
Mrs Damari said the post “gave me a bit of hope that maybe someone does really care about what's going on there”.
“Someone has to do something and take strong action to get them released. And that's the strongest thing I've heard anyone say for a long time.”
She said she hoped Trump would do everything in his power to get her daughter and the other hostages released.