The idea of offering prayers generally is mildly offensive. To mean I am not offended per say, its like a child saying something ridiculous but well meaning, you pat them on the head, smile and say thank you. But these are educated adults who usually have an agenda, even those genuine or ignorant adults who dont believe they have an agenda are still proselytising their religions agenda. The question is what god are they praying to, and what are they praying for?
To maybe make a point, imagine instead of picking the Yahweh god they had picked Satan. So would the families of the victims be comforted by genuine mourners, who said we are very sorry for your loss and will pray to Satan for help?
Imagine a JW watching someone die due to lack of a blood transfusion saying dont worry I will pray for you.
Imagine a catholic priest saying I pray you wont get Aids but you are not allowed to use condoms.
Imagine any religion saying I am sorry your family have been killed but I will pray to a god who could have stopped the killing but chose not to, to make you feel better.
Imagine someone praying to a god who tells you to kill unbelievers. Then after your family are killed another person says I am praying to the same god as the killers did to make you feel better but its ok because I think words written thousands of years ago mean something different than the killers did.
Imagine politicians offering prayers from whatever god is followed by the most voters, do I need to say more, really, they would never do that?
A moments silence is for anyone of any belief (or none) to genuinely pray or not, without offending anyone.
My thoughts are with you, is an offer of sympathy, no strings attached, expressing that there is nothing you can do to help and you wish there was.
Remembrance, is meant to be a respectful time to acknowledge, consider, maybe even regret events in history. Hopefully to learn from them.
Prayers, even genuine ones, are an attempt to say my god will make things better and because I have prayed for you I am a good person and wont even think that I could actually do something to make things better but my beliefs prevent me from thinking about it.
For example prayers in American are usually from politicians to disguise the fact that they could do something to reduce gun crime but wont because it would affect their income from the NRA and votes from the people..
Prayers are a socially acceptable form of ignorance, they hide prejudice and become a gateway to radicalization. We should live in an enlightened society and its just not good enough to be a good person because you believe in a god, we have a duty to grow up and have a superior secular morality.