First of all, you publish a paper, which is very promising abroad. If you do academic work, if you have experience in this field, they will give priority to you.

Secondly, if you are afraid that foreign professors will think you are dishonest. Then you can simply mention it in your personal statement and explain why. In this way, others will think you are a trustworthy person.

Knowing mistakes can make a lot of progress.

In fact, although foreign countries value honesty, they don't have so much energy to expose you. Unless you have a bad personality and are full of loopholes.

Many people go abroad and cheat at home. Why didn't they find out? So, this kind of thing will still happen to people.