When a partner increases (or decreases) their pledge, enter the new amount, then uncheck the Pledge Received box.
TntConnect will alert you when the FIRST gift of this new pledge has arrived. (Technically, TNT will create a thank for the next gift, regardless of the amount; occasionally I have had a partner commit to an increase, but their next gift was given automatically, so I still got the thank you task even though the amount was the old amount.)
TNT will also re-check the Pledge Received checkbox and reset the “start date” for the pledge. This helps the partner’s Average Monthly figure be more accurate.