To find the change in water per minute, we can begin by calculating the rate at which the tank drains.
The tank drains 24 gallons in 6 minutes. To find the amount drained per minute, we can divide the total gallons drained by the total time in minutes:
\[ \text{Gallons per minute} = \frac{24 \text{ gallons}}{6 \text{ minutes}} = 4 \text{ gallons per minute} \]
Since the tank is draining 4 gallons of water every minute, the change in water in the tank per minute is:
\[ \text{Change in water per minute} = -4 \text{ gallons} \]
The negative sign indicates that the amount of water in the tank is decreasing. Therefore, the integer representation of the change in water in 1 minute is:
\[ \boxed{-4} \]