ERJ-170 Flight Attendant reported to the Captain and Gate Agent that two passenger bags with laptops that had lithium-ion batteries were mistakenly gate checked in cargo during boarding. The Captain then deemed it safe to not remove as the devices were off and approved gate departure.

Narrative

During boarding I; the B-FA; was talking to someone who tagged a bag; and then made an announcement to make sure that everyone had all laptops and lithium batteries removed from any gate checked tagged bags. Two passengers; the one I was talking to; and another let me know that they had laptops in their bags. I let the A-FA know what was going on so that he could help monitor what was going on; and the passengers went to the front of the plane to retrieve their laptops. I let the CA and Gate Agent know what was going on when I was able to make it to the front of the plane because the passengers had come back down the aisle and said the Ramp person; or someone; had told them the cargo hold was closed and they weren't going to get them. It's my understanding that all laptops and lithium batteries need to be taken out and are unable to go in that cargo area; so that is when I spoke with the Captain and Gate Agent. The Captain said we would wait. The passengers then came back again and said the CA said that it was ok to go due to the size and them being off. I checked with the CA one last time and he deemed it safe. I was not there for the conversation when they declared it safe; so I can only go with the CA telling me it is safe.If something was deemed safe by the CA then I go with that; but just everyone checking bags beforehand; Gate Agents and also ramp crew not saying no due to potentially just not wanting to get the bag. But if it's declared safe; it's declared safe.