its only on your LOCAL server - you have control over that presumably? After all you made an ODBC connection to remote on it [i.e. your local server], right?
That's presumably because SQL is pulling all the data locally to do the MAX, whereas when you do a date range it does that at the Remote end. Just a guess, might be something else, but there is no way that [I can think of!!] where:
will be any slower than
SELECT Col1, Col2
WHERE MyMaxCol BETWEEN @Param1 AND @Param2
Either there is an index on MyMaxCol in which case MAX(MyMaxCol) will be "instant", and that will also help the RANGE filter, or there is no index - in which case, in both cases, SQL will have to scan every single row in the table.
So if RANGE filter is quick, and MAX is slow, the only explanation (assuming that the rest of the WHERE clause is the same) will be because the fast one was fully processed on the remote and the slow one pulled data locally and THEN did the processing.
But that's assuming apples-and-apples, if there are other variances in the WHERE clause, different JOINs, etc. between the two test queries that would influence the outcome too, of course.