It appears that the Steam client service is asking for permission to run so it can update Steam on your PC. If you have a problem with this, I suggest that you ask Steam support. A recent update to the EA App made it work with Steam. Before that Origin was required.
I have sent a request to Steam & will keep you updated of what they say.
Update
So Steam got back to me and this was their reply:
"Hello,
Thank you for letting us know about your concern, however, to help you with this issue, please contact the EA support team as they are best equipped to resolve any issues you are experiencing with their product.
https://help.steampowered.com/wizard/HelpWithGameTechnicalIssue/?appid=1222670
Steam Support
Niel"
So apparently Steam says it is an EA issue & you all say it is a Steam issue.
