Few would say that, since "this January" is all that is needed. It seems like a mistake. I can't think of a situation in which it would make sense in referring to the past. We say "This January" to refer to the January of this year. "January of last year" is used for the previous year. I think the writer may have changed her intended sentence and forgot to remove "last"

Use of last in this context is highlighting how close the event is to now. It is quite common to use "this/the last" to refer to the most recent of a recurring event such as a day of the week, month or season. It is not remotely necessary, but it is quite normal.

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