Security of information
Assuming the voice path is routed through a centralised infrastructure offered by the provider of this service the implication would be that the audio could be intercepted / recorded by that provider. Based on the published information it is reasonable to assume that throughout the duration of the whole call (queuing and talking to the remote party) the audio remains routed through this solution.
If you consider a lot of contacts to call centre environments are to organisations (e.g. your bank) where you go through identification and verification procedures disclosing personal information including security details this raises interesting questions on the security of your information and consequent liability if the organisations in question were to blame the caller for disclosing the information through the use of an intermediary service i.e. could the consumer become liable for the loss / fraud as a result if the details are compromised.
Note - There is no suggestion that the provider is doing anything malicious or that there are any security issues with regards to the solution itself just a question on the technical architecture and how it may fit with data security and legal frameworks