Basically, it has no effect. To tell the truth, you'd better make one. The company is right. When you don't have a work permit, you will be affected in many ways. For example, without proof of foreign population, you will be restricted in many aspects such as finding a job. As for the influence, there is no bad influence. When you go back to your original place, just put the foreign certificate. Even if someone investigates your file in the future, they won't care about this. Don't worry.