According to our current understanding of the laws of physics, causality is a fundamental principle that cannot be violated. Causality states that an event cannot have an effect that travels faster than the speed of light. In the scenario you described, where two ships are in different time-dilated fields, and Ship A sends a probe to Ship B through a less time-dilated field, it may seem like the probe arrives before light through the time-dilated space, potentially raising concerns about causality.
However, it's important to note that time dilation does not allow for the violation of causality. Time dilation affects the passage of time and the perception of time between different reference frames, but it does not enable the violation of causality by allowing information or signals to travel faster than light.
When Ship A sends a probe through the less time-dilated field to Ship B, it may indeed arrive at Ship B before light traveling through the time-dilated space can reach it. However, the arrival of the probe does not enable Ship A to communicate or send information back to Ship B faster than the speed of light. Any communication or interaction between the two ships must still obey the fundamental limit imposed by the speed of light.
Therefore, even though the probe may arrive earlier from Ship A's perspective due to the time dilation effects, the principle of causality remains intact because the probe's arrival does not violate the limit of the speed of light for communication or the transfer of information.