Is there a way to verify the URL of a page loaded in a browser window inside an iPhone app?
Two Questions:

Verify URL

Connect through laptop. Use packet sniffing tools to check what requests go out.

Perhaps: Disable 3G. Wrap with WiFi in Faraday cage, make sure no other covert incoming or outgoing communication.

Eavesdrop

Cat and mouse. Basic tools and basic skills will detect basic phishing/eavesdropping. But the above URL verification would not catch other simple methods like the website re-broadcasting it elsewhere, or the app recording and transmitting at other times.

Still, you could read the EULA.

Given what is currently known about Apple and Google, Verizon and AT&amp;T, Paypal and credit card companies, your ISP, business focii, data breaches, government agreements, other gov't interactions, etc. it is probably safest to assume that everything is tracked and recorded, whether you are using the phone or not.