All alerts and all viewable inquiries from myFICO are hard pulls. The only place you can view softs are directly from equifax.
SW alerts only provide a net score change and those 10 points may not be directly linked to that inquiry. For example, I once got a SW alert for +20 because I added an inquiry. Inquiries don't increase your FICO but it was a dropped baddie that led to the net increase when I received the alert for my inquiry. In other words, some (if not all) of the loss could be linked to the inquiry, but other things could be happening like increased balances or other changes.
With that said, I would take steps to get it removed. They are allowed to report. If you are working with them I'd send a letter asking them to delete the iqnuiry (and of course delete the TL if they are reporting).
The FCRA is structured with the express purpose of permitting credit inquiries without prior express permission of the consumer.
That is the purpose of section 604. It defines those types of inquiries for which a party who has a permissible purpose can request the consumer's credit report without prior express permission from the consumer. The "permission," if you wll, is inherent in the consumer's relationship with that party.
Otherwise, credit and business transactions would come to a crawl.
A so-called soft pull is one which is not viewable by others who pull your CR. That includes pulls for FICO scoring, and thus they dont count in your scoring.
The only type of permissible purpose that is specifically excluded by statute from view by others are inquiiries related to unsolicted offers of credit or insurance, and the inqiree may receive only the consumer's name and address.
Coding of other types of permissible purposes in a way that blocks their appearance in credit reports viewable by others is strictly an administrative conconction of the CRAs, for which there are no published rules or procedures. Some are widely recognized and consistently applied, such as a consumer's pull of their own CR or a pull by an existing creditor that relates only to their own internal account review. Others seem to have no rhyme or reason, such as a consumer initiated request for new credit that the creditor somehow is able to obtain coding as a soft pull.