I think you are misunderstanding. They were not to be unsettled at some alleged letter that was supposed to come from them regarding the DOL had already come.
Now in regard to the coming of our Lord Jesus Christ and our gathering together to meet Him, we ask you, brothers and sisters, 2 not to be quickly unsettled or alarmed either by a [so-called prophetic revelation of a] spirit or a message or a letter [alleged to be] from us, to the effect that the day of the Lord has [already] come.
As far as the Apostles are concerned there is no difference between his coming and the day of the Lord.
Chap1 clearly has those who reject the Gospel being banished from his coming presence on the day we are glorified in him.
This also happens in chap 2...,highlighted below.
6 And you know what restrains him now [from being revealed]; it is so that he will be revealed at his own [appointed] time. 7 For the mystery of lawlessness [rebellion against divine authority and the coming reign of lawlessness] is already at work; [but it is restrained] only until he who now restrains it is taken out of the way. 8 Then the lawless one [the Antichrist] will be revealed and the Lord Jesus will slay him with the breath of His mouth and bring him to an end by the appearance of His coming. 9 The coming of the [Antichrist, the lawless] one is through the activity of Satan, [attended] with great power [all kinds of counterfeit miracles] and [deceptive] signs and false wonders [all of them lies], 10 and by unlimited seduction to evil and with all the deception of wickedness for those who are perishing, because they did not welcome the love of the truth [of the gospel] so as to be saved [they were spiritually blind, and rejected the truth that would have saved them]. 11 Because of this God will send upon them a misleading influence, [an activity of error and deception] so they will believe the lie, 12 in order that all may be judged and condemned who did not believe the truth [about their sin, and the need for salvation through Christ], but instead took pleasure in unrighteousness.