In 2161 time travel is common place, but highly regulated, when he’s shot, a cutthroat businessman’s consciousness is sent back in time by his life insurance company to prevent his upcoming murder, without disrupting the timeline too much or his provider cancels his contract.

"In 2161 time travel is common place, but highly regulated, when he's shot, a cutthroat businessman's consciousness is sent back in time by his life insurance company to prevent his upcoming murder, without disrupting the timeline too much or his provider cancels his contract." (44 words)

This version includes a bit too much background, making it too long. I suggest taking the previous version, "A cutthroat businessman is sent back in time by his life insurance company to prevent his murder in 7 days." and adding a few adjectives and the inciting incident which will help.
First, a breakdown:

Inciting incident: "when he's shot," ---> This is a good inciting incident, it's simple. But I'm not sure it's the correct one. If the goal is to to prevent his murder by traveling back in time, then I suggest that his company sending him back in time is the inciting incident.

Protagonist: "a cutthroat businessman?" ---> Good.

Goal: " to prevent his upcoming murder, without disrupting the timeline too much or his provider cancels his contract." ---> Why does his company send him back? What must he accomplish by preventing his murder? I think that would be the more suitable goal. It's good to include the stakes of what happens if he doesn't accomplish his goal, but what is really the point of sending him back?

For example:?After his struggling company sends his consciousness back in time, a cutthroat businessman must kill their top competitor to prevent her from securing a multi-billion dollar contract or else be executed. (31 words)

When you mentioned sending his consciousness back in time, it reminds me of "X-Men: Days of Future Past"(2014).

"A cutthroat businessman is sent back in time by his life insurance company to prevent his murder in 7 days." (20 words)

Inciting incident: None described ---> I think this logline would benefit from an inciting incident. Why does he need to prevent his own murder? I think including the inciting incident would help give this context. As a general rule, I believe most loglines should describe an inciting incident, but the only ones which can get away without are romance and drama loglines. Action, fantasy, sci-fi, etc should describe an inciting incident to help give a reason why the protagonist pursuing their goal.

Protagonist: "A cutthroat businessman" ---> Good. But, if the character has a an arc, you may want to use an adjective which helps to imply that arc.

Goal: "is sent back in time by his life insurance company to prevent his murder in 7 days." ---> I mentioned the lack of context above. What catches my eye is 'life insurance company'. I know it's a labeled as 'SciFi', but this is something that stands out; as far as I know, along with most people, we don't think or believe that life insurance companies have time machines. I suggest either using an adjective, or changing it to generic term.

Antagonist: Implied to be murderer ---> Okay.

Overall, I think this attempt needs a little tweak, and should have an inciting incident added, but overall it's good.
The question I have, is this the 'A' story? Above, it sounds like the main conflict is trying to fix the deal, but in this version it's trying to prevent his murder. What do you consider to be the climax of your story? Is it when he faces the person/group who murder him? Or is when he is about secure the agreement?

"When he's killed, a cut throat businessman is sent back in time 7 days by his company to prevent his murder, but must preserve the agreement he secured for his firm, that may have gotten him killed, or the deal is off." (42 words)

Inciting incident: "When he's killed, a cut throat businessman is sent back in time 7 days by his company to prevent his murder" --->I am a bit confused. If he's already dead, how can they send him back? But anyway, the inciting incident doesn't seem to be when he's killed, it's when his company comes to him to send him back. This part can definitely be reworked to for clarification. From mikepedley85's review, it sounds as if there was a previous version of this logline which was edited. I think the phrasing of his example works much better.

Protagonist: " a cut throat businessman" ----> I believe 'cut throat' is one word, at least in the way you're using it. Otherwise, this is okay.

Goal: "must preserve the agreement he secured for his firm, that may have gotten him killed, or the deal is off." ----> The logline seems to put too much attention on the protagonist trying to stay alive. It looks to me like the reason for him to continue and pursue his goal is because he doesn't want to die, but those are just the stakes. His objective, the goal of the story is described as "must preserve the agreement he secured for his firm,". Now, the problem with that is that it is a bit confusing. If he already made the agreement, why does he need to preserve it? If this is the goal, then doesn't that mean that the inciting incident?should be the whatever happens to the agreement?

Think about it this way. The goal: "must preserve the agreement he secured for his firm,". Why must he pursue this goal: Because he's killed and his company sends him back in time.

I think it lacks a causal relationship. It seems very close, as if the logline describes an event that is close to the inciting incident, but I'm not sure it's the actual one. The logline answers why he's?sent back in time, not?why he must preserve the deal.?In this logline, the goal described could be switched out for anything. He could save someone else from being murdered, go to murder someone else, etc.

Here's an example: After his milestone arms deal falls through, a ruthless businessman must be sent back in time to secure the agreement for his firm.?(23 words).

I know, I cut out a lot. But to me, that seems to be story in it's simplest terms. (obviously I made up some of the stuff, such as 'arms deal'.