Arvind,
Are you using SPM environment ?
Generally, you will be activating the compliance checks from EWM to GTS via PPF actions in EWM.
Once the above activity is complete then EWM will try to make a call to GTS.
Now what you need to figure out is, How the business partners are being setup in EWM .
If they are same as ECC and they have been transferred to GTS from ECC then you don't need to do any additional configuration for partner mapping and just add the logical system to the logical system group and should be good.
If the partner number is not same between EWM and ECC then you need to define the mapping here and I don't think that is the case.
The config screen shot you have shown here generally used for legal unit mapping or partner mapping i.e. TM to GTS - export declarations and not generally meant for customers/vendors.
Please do let me know if you have any questions. Thanks.
Regards
Raj