Hi Monica
The OOTB Status attribute on the Project Object gets its values from the "Investment Object State" Lookup.
The "Submitted for Approval" Value in this lookup is used only on the Idea Properties Page and Filter Page. It is not to be present on the Project create or Properties page.
You could create a custom lookup if you would like to add additional values other than Approved, Not Approved, and Rejected.
Thanks
Shailey