1 - This would have broken her Oath to not betray the BA.

2 - The waygate in question is thought to be guarded/secure. My guess is Hanlon and the 2 escaped BA compromised this security, under the orders of one of the FS (Demandred imo).

You're right though, it's very strange that Verin missed this - but then again, Verin didn't know how much Mat changed after his time with Tuon (actually, it was mainly Joline/Teslyn/Edsina which seem to have driven him to avoid all things Aes Sedai).