So, I was trying to see this picture on the phone.
It is hard to say. While generally I would agree with others to replace the tire, I must add the damage is n the "rim protect" bar.
How deep does it go? Is it flush with the side wall? Is only the rubber rim/bar stripped?
For sure the tire will be a bit softer there. However, if the damage did not penetrate any deeper than surface of the side wall, you might be OK.
On the other hand - if you are spirited driver and like tight quick turns - replace it. Otherwise - see above again.
^^ You're right, the tire store will likely say "replace, replace." For one thing, their lawyers demand they do the low-risk option.
For another thing, the cost of replacing it is far lower than what could happen, even on a good day, should it pop at the wrong time. Think ruined rim, slide into curb, damaged suspension components...