I will check with them and let you know. Generally implies that the second ‘I’ is understood, hence repetition can be avoided. Can also mean that apart from me anyone else would/could let you know..if required.

Can I check with team?

I will check with the team and get back to you vs I will check with the team and let you know. I will check with the team and get back to you is the most popular phrase on the web.

Will definitely look into it?

The official meaning of “I will look into it” is that “you don’t the answer, but you intend to find out.” Alternatively, like “sure,” you can use “I will look into it” as a way of trying to end the conversation, as a polite way of saying that you either don’t know the answer or have no intention of sharing it.

Will let u know soon?

If you want to say you will let someone know something at the first possible opportunity, you would have to say: “I will let you know as soon as possible”. “I will let you know soon” is also possible, but does not convey any particular sense of urgency.

Is just to let you know rude?

Yes it is correct and no it is not necessarily rude. For example I might say to my boss while processing a sale, “Just so you know, it looks like the inspection contingency on this is only 5 days instead of 10.” He will probably thank me for pointing out this fact because it is important and he might not have seen it.

Will check it out meaning?

to examine or try something; to think about something. It’s something we all have to be concerned with. Check it out.

Will check with him meaning?

To Check With Someone Meaning The phrase check with someone means to verify something. If someone needs to check with someone, he will usually do this prior to taking action. Checking with someone may also be used to refer to asking for permission to do something.