Is it possible to download the data in Compare and Deploy grid into an Excel file. Or any way to implement a custom report around it to download the data in that grid?
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No. What are you trying to achieve?
It's not a hard and fast and really a requirement. Just a curious want to ease the tracking of object changes.
Stefan is correct that there isn't a way to do this, but I'd definitely be interested in understanding more of your use case. How would you use the exported Excel data? Do you have some other repository where you're storing information about your design objects?