It is important to know your audience when using the word remit as the word has different meanings in the US and UK (and consequently for those using one style of English or the other.)
In UK English the word remit refers to a set or area of responsibilities. It would therefore be perfectly appropriate to say the following: “Unfortunately, I am unable to supervise the preparation of the company annual accounts as this is outside my remit.”
However, in both the US and UK, remit means either to restore to a former position, to refrain from extracting something, e.g. a penalty, to pardon, or (in law) to refer a case to another court for consideration.
Therefore, remit could be used for example as follows: “The case was remitted to the family court as it involved issues relating to the children.” However, in the US it is more common to use “remand”, for example. “The court of appeals remanded the case to the trial court with directions to modify the conclusions of law and to enter judgment in favor of the defendants.”