The thing works by encrypting a file using a password derived key (if I understand correctly) which then gets uploaded to their infrastructure. You get the url, containing the password (used to derive the key). There's no point and no way tricking you into sending it to them, i.e. setting up a MITM attack.
The client could just leak the key, but as far as I can understand, it's open source so you can prevent it by building it yourself (and either trusting others or auditing the code yourself too).
As the password is in the URL and you'll send the url through another channel, there is no way to MITM it (decode and then recode for the recipient). And wouldn't make sense anyway, since there was no key exchange, the recipient does not provide the sender with a key to use.
So yeah, they can absolutely look into your files - if they steal your key. (They could do it on the receiving side too, BTW.) But you can't sidestep this with any encryption software: you have to trust at least the encoding and decoding app. (Also, I think you can self host this.)