Often a Client will want to see what the breakdown is for their own cost data management and benchmarking purposes, although an Activity Schedule doesn't always assist with this, depending upon how it is structured. It may also be a simple request to allow a comparative review between tenderers, for evaluation purposes.
The procurement obligations differ between public sector bodies and private organisations, which you don't mention in your question. However, maybe just ask the Client why they want the information, which allows you to understand the nature of the request.
I am assuming that the tender evaluation criteria has already been set out clearly, so not sure why this would affect your Quality Submission score, unless there was something specifically related to the Activity Schedule. If your score was reduced accordingly, then you may have grounds to challenge the decision even with a private organization, which should have detailed governance procedures by which they operate. This may not lead to the outcome you hope for, but it would certainly raise issues of non-compliance within the organisation that they would hopefully address.