To actually fix the problem and not lose any data (provided that that tree is the only missing object, which I doubt) you could try this:
- checkout the parent commit of the commit with the concerning tree
- try git cat-file -p with the name of the problematic commit to see what the commit message says (hopefully it will tell you what changed)
- now you might be able to determine the changes that were made and from this the directory structure can hopefully be inferred.
- if 3 worked, then you can create your tree manually using a text editor and a zlib compressor. The entries in the tee file will be other tree objects or blobs. Hopefully most of the files and folders are shared (have no changes) between the two commits. This will allow you to reuse most of the entries from the tree object of the checked out commit.