The legal provisions on the refund of fees by extracurricular training institutions mainly involve contract law, consumer rights protection law and other laws and regulations. According to these regulations, the contracts signed between extracurricular training institutions and students should be legal, fair and transparent, in line with national education policies and relevant laws and regulations.

In terms of fee refund, extracurricular training institutions should reasonably refund students' tuition fees according to contracts and relevant laws and regulations. Specifically, the refund provisions include the following aspects:

1. Refund period: Extracurricular training institutions shall refund students' tuition fees within the time limit stipulated in the contract. If the course cannot be started normally or the contract cannot be continued due to institutional reasons, the students shall be informed in time and the fees shall be refunded as agreed.

2. Refund standard: Extracurricular training institutions will refund the fees according to the refund standard agreed in the contract. Usually, the refund standard includes the agreement on the proportion, time and method of refund.

3. Liability for breach of contract: If the extracurricular training institution fails to fulfill the obligation of refunding fees as agreed in the contract, the trainees can complain to the relevant departments or bring a lawsuit to the court, and ask the training institution to bear the corresponding liability for breach of contract.

4. Handling of special circumstances: In some special circumstances, extracurricular training institutions can be exempted from the responsibility of refunding fees, for example, students cannot continue their classes due to their own reasons, and courses cannot be started normally due to force majeure.

In addition, according to the Law of People's Republic of China (PRC) on the Protection of Consumer Rights and Interests, students should enjoy a series of consumer rights and interests such as the right to know, the right to fair trade and the right to safety when spending in extracurricular training institutions. In the process of fee refund, if the extracurricular training institution infringes on the consumers' rights and interests of the students, the students can complain to the Consumers Association or relevant departments and ask the institution to bear corresponding legal responsibilities.

To sum up, the legal provisions on the refund of fees by extracurricular training institutions mainly involve the relevant provisions of the Contract Law, the Consumer Protection Law and other relevant laws and regulations. Students should carefully read the terms of the contract when choosing extracurricular training institutions, understand the refund regulations, and keep relevant evidence during the refund process to safeguard their legitimate rights and interests.