Should I be concerned about strange, new iPhone app appearing after repair?

Unless you can come up with some other explanation of how this happend, it sounds like your phone has been infected by some malware. It's impossible for us to say if the infection was the result of something the factory did or something you did. Either way, you should be very concerned. I'd recommend the following course of action:

• Make a backup of any data you have on the phone. (The backup could be infected, see this question, but if you have no earlier backup you either have to take the risk or lose your data.)
• Do a complete factory reset, wiping the phone clean.
• Change any passwords that has been stored on or entered on the device.

While you are only seeing one app, it might just be a symptom of a deeper infection. Just removing the strange chinese app may not be enough.

I would be very concerned. One thing I have learnt about security, in all the years I have been trying to understand it, is that if you didn't put something there, somebody else did, and if you don't know what it is doing then the only thing to do is reset, reinstall, and be happy with everything. If you don't know why that software is there, be assured, somebody put it there for a reason and it may be a good reason but it isn't your good reason so if that phone was mine I would save all my data, and only my data, and completely factory reset it.

Yes, and be concerned about more than your phone.

I can’t imagine a situation where an app was installed without your pin/password. without them first jail-breaking or otherwise significantly compromising your phone's OS. I think the only safe assumption is that anything your phone had access to, they also had access to.

So any account your phone has access to is suspect. Particularly any email account you have setup. Look for password reset emails, check your sent items etc. If you had any kind of financial app ( bank etc) check for odd transactions etc.

If that all looks fine, I’d follow the advice of others in terms of resetting the phone, but also go beyond the phone and reset all your important passwords etc.