Seemingly, not at all.

WWE have just added The Miz's "Christmas Bounty" film to the WWE Netflix collection in the USA. The Wrestling Observer reported that people would expect WWE to remove content from Netflix due to the WWE Network launching.

This isn't the case however. WWE/Netflix connection is said to be fairly lucrative to both parties and there is no need to pull anything given the revenue generated by the features. WWE and Netflix will continue to work with each other for the foreseeable future due to this.