Can a party to a suit who is non- aggrieved file an application under order 9 rule 13 ?

File objections to application and oppose the court orders, allow or it dismiss it.

Actually the said application was already about by the court and now we have approached the hon'ble high court against the Impugned judgment. 

The party to a suit who was set exparte by court due to his absence, has rights to get the exparte order set aside and he can very well contest the case in his individual capacity.

You cannot object to it other than if it is delayed and he has not filed a petition to condone the delay.

If you have approached high court, you may better pursue that and wait for the result, though your applicaiton before high court may not be entertained by high court since it is a justified right of that  party. 

True, that would be justified in case the party had some locus. 

The fact is : 1) The party were originally defendants 1&2.However, during the pendency of the suit, they relinquished their rights in favor of defendant 1 . 

2) Although the parties were not removed from the  "array of parties".

3) Now they have no interest in the suit after Relinquishment deed was signed. 

4) They would have the right to file O 9 R 13 if they had disputed the Relinquishment Deed, which is not the case here. 

5) There is a specific judgment of Allahabad High Court in this regard. 

2000 SCC OnLine All 827

Gauresh Ahuja
Versus
Mohd. Ayub and Others

6) I'm searching for an Apex Court judgment in this aspect. 
 

If they were impleaded as necessary parties to the suit,  their relinquishment of rights in the property would not dis entitle them to contest the case. 

Your objections to their rights to challenge the case as defendants can be treated as deprivation of their rights. 

The court will not entertain your objection. 

Besides it is against natural justice too 

If you are plaintiff then you would have filed application to strike out them as un necessary parties in plaint when they filed application.