How does your company deal with customer service issues caused by a third party?

EVERY TIME WE DEAL WITH THE CUSTOMER LIKE OUR OWN CUSTOMER WE DONT CONSIDER IT THAT IS THIS OUR CUSTOMER OR THIRTD PARTY CUSTOMER

I agree that the company needs to step into to attempt to resolve the issue from the perspective of good customer service.
It really is upto to the third party supplier to provide service recovery measures when the error rests with them. 
A complacent third party supplier with mounting complaints and poor service standards needs to be replaced swiftly !

"What you need to do...", how does your company deal with customer service issues caused by a third party? The end result is always for the customer to have a good customer service experience from a company.
Anything which affects the potential good customer service of customer needs to be investigated.
This is especially true if the issue has been created by a third party.
If the third party issue is not resolved, it leaves room for the same issue to recur.
Customer service is all about improving service and potential problems which could affect reputation of company.
After all, it could be that the customer is actually right and maybe the third party or company has overlooked some area of product or service.
Company is responsible for the business dealings it has with third parties and there is an agreement between the two that one will provide a product/service and the other will make it available to customers.
In effect, third parties are also part of the business transaction.
Important for good communication to take place and be maintained between the company and third parties.
If there is a breakdown in this agreement or if the customer believes that something has gone amiss or is not good enough, the company has to take serious this matter and proceed to take steps to look into how things can be improved to the satisfaction of the customer and lessons learnt for the future.

Remind your3rd party of his responsibility and point out the details of your contract.  Lets hope it was a good contract from the start.  Work with them to fix the problem before you start looking elsewhere for support

I call for a meeting for us, the customer, and the other parties to identify the problem and it's resolution to the customer's benefit. This approach worked for me so far. I see it a s win all proposotion all of us vendors have a vested interest in the customer's success.

You should have a customer experience management plan to handle third party influencers.
They influence a lot and either take away or bring more customers.
Most of the companies ignore this aspect because of lack of data and method or simply not ready to work on 'inclusive method'.
Third party customer experience influences are highly visible in high value products.
I have developed a system along with a colleague of mine and included this third party issues in our customer experience management.
I can help if required.

 set some conditions related to costumers servise orginize to deal with him . 

set clear process with services provider and dfine punch mark for Quality and quantity .

Every cpompany is having a service provider which is directly or indirectly dealing with customer in the front end or back end. The third party issue will also affect the customer service. If the issue is due to the thirdparty we cannot tell the customer that it is because of the thirdparty service provider. We have to admit it as our mistake and take action to make the service done with customer. Admit the issue and solve the issue with a better offer to the customer.

Customer is always right. His or her complaints issues need be addressed promptly and approximately by all. There is no third party customers. All are our customers. Period

OUTSOURCING has become a common business practices in the modern world.
Many services are outsourced to the third parties at all levels.
For e.g., Marketing & Sales, After Sales Service, Data Entry, Technical Clarifications on a Product / Service, Security, Job Work, etc.
Really a lot of works are outsourced or delegated to the third party.
This is the common scenario.
Now the question is who is responsible for a problem that is caused by a third party? ABSOLUTELY the ONUS lies on the owner of the product / service! It is because the customer goes by the product / service based on the BRAND / NAME.
He is not aware about outsourcing, and, he need not know that! The Company should take EVERY RESPONSIBILITY, whether training or education or proper AWARENESS are given to the third party.
When something has gone wrong, the company should analyze the situation and RECTIFY the mistake at its own cost and effort!