when the guy in store suggested to just delete it I did it without thinking. Here's the link to icon I found that looks the same, I suppose it's UC Browser. As I mentioned, everything was in Chinese, including name of the app. – Rafi Rosa
Yes, it was UCBrowser. This is a popular browser in China (since Google Play/Services are not available there) most Chinese phones actually come with this browser pre-installed.
I believe it was perhaps a way for the repair guy to test the phone in a familiar app... UCBrowser was found to have several flaws that would allow others to exploit, but mainly they'd only happen if you actually used the browser.
I have done a complete factory reset of my phone and changed all passwords that I used while using it. After that all of apps I have previously installed were restored by iPhone and all of my files were stored on iCloud, is it all I can do? – Rafi Rosa
I believe you did well. Even if it was just an app that the repair guy decided to use for testing, he might have done a lot more than just installing and using the browser. Not being honest/upfront about what they really did when they just needed to repair a battery is certainly not professional.
A factory reset and passwords change should be safe enough regarding your data. If the store does not have ways to profit from replacing other hardware in your phone, you won't notice any difference. However, if you need to be completely sure about its integrity perhaps a certified Apple store may perform a check and tell you what was really changed (not sure if they do this though).