The fiscal sponsor must be a 501(c)(3) organization as recognized by the IRS. The fiscal sponsor cannot be an organization whose tax-exempt status is pending. The sponsored project must be able to qualify for exemption under section 501(c)(3), even if the project has no intention of ever applying for it.
Pressing the Ignore button on the listed invitation on the LinkedIn site is effectively a soft rejection. The message then moves to your Archived folder. You can later choose to open the message again and accept the request.
For example, this is the email: The is no equivalent if someone declines. The only choice is therefore to wait and see if they accept your invitation at some point. As people may only be logged into LinkedIn intermittently, this could be some weeks or months after you sent the invitation.