As we watch through the 2016-2018 streaming TV series Timeless it's fun to see the little changes to history the writers include as consequences of people time-traveling to the past and mucking with key events in history.

Recall the format of this show is a cat-and-mouse, adventure-of-the week serial where two teams are chasing each other through history. One team is trying to change history, acting from motivations that are slowly revealed, while the other is trying at the same time to keep history's major events aright.
For example, in S1E1 the teams traveled to the site of the Hindenburg disaster. The end result was the Hindenburg did explode... but it happened a day later, after the maiden voyage succeeded, and it was attributed "terrorists" who used a cheekily 21st century moniker. The characters' use of hastily-imagined fake names when they're trying to patch things up— names that then become part of the historical canon that everyone in the (new) present day knows— seems to be a minor running gag. As do black-and-white photos or artistic renderings of the modern characters standing at the edge of the scene in newspaper reports. I like it.
Now, if Lucy's emotional takeaway from this was, "Waaah! My whole live I've been lied to!" I wouldn't mind it. It'd be a little trite, sure— because it feels a bit overdone— but I'd take it in stride. What happens instead is that Lucy focuses on, "They took my sister and I want her baaaaack!"
This emotional beat of "My sisterrrrrrr!" becomes irritating because Lucy harps about it every single episode. And that's frustrating because she, an otherwise very smart person, is written as completely unable to reason about what has happened. She harps in every episode to multiple characters about how she needs to use the time machine to "save" Amy. But there's nobody to save. Amy hasn't been killed. She hasn't been kidnapped, stolen, or harmed. The simple fact is Lucy's now in a timeline where Amy's parents never met. Amy never happened. Going back and changing that with a time machine is a vastly different proposition than, say, preventing an accident or stopping a crime. The writers write Lucy as too daft to get this... and by extension treat us viewers as unable to see the difference, either.

Recall the format of this show is a cat-and-mouse, adventure-of-the week serial where two teams are chasing each other through history. One team is trying to change history, acting from motivations that are slowly revealed, while the other is trying at the same time to keep history's major events aright.
For example, in S1E1 the teams traveled to the site of the Hindenburg disaster. The end result was the Hindenburg did explode... but it happened a day later, after the maiden voyage succeeded, and it was attributed "terrorists" who used a cheekily 21st century moniker. The characters' use of hastily-imagined fake names when they're trying to patch things up— names that then become part of the historical canon that everyone in the (new) present day knows— seems to be a minor running gag. As do black-and-white photos or artistic renderings of the modern characters standing at the edge of the scene in newspaper reports. I like it.
Stop Whining about Amy!
One timeline change the showrunners created that I do not like is the disappearance of Amy, the younger sister of one of the main characters, Lucy. When Lucy returns from her S1E1 mission involving the Hindenburg she finds her sister isn't home... and her mother says Lucy never had a sister! One of the other characters does some research and finds that, in the new timeline, Lucy's mother never met her father. He married instead a woman descended from a new survivor of the Hindenburg disaster. "So how am I still here?" Lucy asks. Answer: the man she's always known as "Dad" was only her step dad, and Amy was only her half sister.Now, if Lucy's emotional takeaway from this was, "Waaah! My whole live I've been lied to!" I wouldn't mind it. It'd be a little trite, sure— because it feels a bit overdone— but I'd take it in stride. What happens instead is that Lucy focuses on, "They took my sister and I want her baaaaack!"
This emotional beat of "My sisterrrrrrr!" becomes irritating because Lucy harps about it every single episode. And that's frustrating because she, an otherwise very smart person, is written as completely unable to reason about what has happened. She harps in every episode to multiple characters about how she needs to use the time machine to "save" Amy. But there's nobody to save. Amy hasn't been killed. She hasn't been kidnapped, stolen, or harmed. The simple fact is Lucy's now in a timeline where Amy's parents never met. Amy never happened. Going back and changing that with a time machine is a vastly different proposition than, say, preventing an accident or stopping a crime. The writers write Lucy as too daft to get this... and by extension treat us viewers as unable to see the difference, either.