The team currently has $14$ wins and $11$ losses ($25$ games played), with $12$ games remaining for a total of $37$ games.

To win more than $50\%$, the team needs more than $\frac{37}{2} = 18.5$ wins, so at least $19$ wins.

The team already has $14$ wins, so it needs:

$19 - 14 = 5 \text{ more wins}$

Verify: $14 + 5 = 19$ wins out of $37$ games. $\frac{19}{37} \approx 51.4\% > 50\%$. With only $4$ more wins: $\frac{18}{37} \approx 48.6\% < 50\%$.

The least number of remaining games the team must win is $5$.