Something boring but workable is using CSV files, dropped to a location on customers end through SFTP containing your transaction IDs that you are interested in.
If its MS SQL Server on the other side, then a SQL agent on that server using some SSIS can read the CSV as input and prepare your required output as a CSV again for you to pickup from their SFTP Server.
Yes, we did this at a few places and it's boring and low tech and... works extremely well. Loose coupling, very small interface, and bad behavior on either side doesn't impact the performance of the actual DB, etc.
This works in some situations but the OPs use case seems to suggest near real-time access to records that would only have recently been created. I'm unsure if CSV could work well here.
