No, updating your dashboard does not impact your credit score.
When your credit score updates on your profile, Upstart has conducted a "soft credit inquiry" of your credit information. This is not recorded as a new inquiry on your credit report and is not reported to other companies, including lenders, that view your report.
Just a note, when you check your credit report, you may see the soft credit inquiry. That is so you have visibility into which financial institutions are pulling your credit information and for what purpose. When you apply for credit (or a new apartment, or a new cell phone contract), the people who view your report won't be able to see your Financial Fitness Dashboard inquiries.