What do computers and rapper, fifty cent have in common?

2 bits = 50 cents

Well, if you think that spilling 3 months of data into tempdb to begin with is better, try it...   I'm not sure that's the case.   A lack of indexes is...

Those twp tables are not identical.

Without knowing why they wanted a Linked Server in the first place, I'd resist creating a 2nd one.  What are they doing with it?   What SQL instances do the reporting...

The problem is GETDATE().   It's not going to return the first of the month.  Try this:

DECLARE @Today AS date = GETDATE();
DECLARE @FirstOfTheMonth AS date = DATEFROMPARTS(YEAR(@Today), MONTH(@Today),...

So what's stopping you from using two columns instead of just one, and not wasting an additional column at all ?