Jiraiya Traitor? This is the reason why Jiraiya doesn't use Konoha's headband! Anime#16
The headband is a symbol that shows the loyalty of a shinobi to their country. And if someone has tarnished their headband, then they will be said to be unfaithful to the State. Then what about Jiraiya's headband?
As you can see for yourself, Jiraiya has a headband that is different from other shinobi. In Jiraiya's headband there is a kanji "油" which means Oil. Can Jiraiya be said to be a shinobi who is not loyal to his country? Of course not. Let's look at this.
At a young age, Jiraiya always used a headband with the Konoha symbol. And with 2 friends, Orochimari and Tsunade always fought together, and participated in the 2nd Shinobi World War.
Jiraiya is also not an ordinary shinobi, he has got special rights that can do whatever he wants. He was also known as a great eye, so it was possible that Jiraiya was wearing a headband so it would not be detected that he was from Konoha. And not many people know also about Mount Myobokuzan.
This is just our personal opinion that we can conclude with our experience and some clear sources. For the right or not reasons above, it is from you alone. Greetings Dattebasa!