IMPORTANT In order to delete a budget/scenario you need to OWN the company (or have the proper manage rights), not "share" the company. Review that you are indeed the OWNER of the company first before deleting a budget/scenario   

Access your company list: 

Then, tap the recycle bin to the right of the budget you do not want to keep in the My companies section.

CAUTION: This operation is irreversible.

Related Articles (Please refer to the links below) 

- How to SELECT a budget

- How to ADD a blank budget

- How to RENAME a budget