This is an inappropriate usage of got.
The tense is less the problem than is the ambiguity of the definition of "to get."
The true meaning of the automated response is something like:
- We already got (i.e., received) an open dispute for that trade.
- "got" = simple past.
- Definition of "get" = to receive.
- We have already gotten (i.e., have received) an open dispute for that trade.
- "have gotten" = present perfect.
- Definition of "get" = to receive.
The usage of "got," however, is inappropriate because the ambiguity of its definition (not its tense) allows the reader to construe another different, unrelated meaning:
We already got (i.e., obtained) an open dispute for that trade.
- "got" = simple past.
- Definition of "get" = to obtain.
We have already gotten (i.e., have obtained) an open dispute for that trade.
- "have gotten" = present perfect.
- Definition of "get" = to obtain.
Before, in the first and accurate meaning, "We" referred to the recipient of the open dispute. That recipient was the regulator of trades and any subsequent disputes between trading parties.
Q: What were they doing with or to the open dispute?
A: Receiving it at some point in time.
Now, in the second and inaccurate meaning, "We" refers to a party who submits a dispute request for the regulator to open. They are now a trader, not a regulator.
Q: What were they doing with or to the open dispute?
A: Obtaining it at some point in time.
To answer your last question: Yes, this is formally ambiguous but likely obvious in meaning to speakers of American English who have more context than just the question. To ensure clarity you may simply not use the verb "to get" at all, and instead use a more precise verb.