The 38-year-old fisherman already knew the attack was serious: he joined civilian vigilantes to defend the town but their simple weapons were no match for the Islamists' superior firepower.
"People fled into the bush while some shut themselves indoors," he said of last Saturday's attack.
"The gunmen pursued fleeing residents into the bush, shooting them dead," he told AFP from the Borno state capital, Maiduguri.
But it was only after breaking cover on Tuesday night that he realised the true scale of the attack, which it is feared may be one of the worst in the six-year insurgency.
"For five kilometres (three miles), I kept stepping on dead bodies until I reached Malam Karanti village, which was also deserted and burnt," he said.
Local officials this week said the attack forced at least 20,000 people from Baga and other settlements in and around Lake Chad to flee, many of them across the border.
Nearly 600 others had been stranded on an island on the lake without food, water or shelter.
The attack wasn't the first on Baga. Nearly 200 people were killed in April 2013, when militants stormed the town and set much of it on fire, prompting fierce fighting with the Nigerian military.
This time, the Islamists met less resistance and were able to take over the town and overrun the headquarters of the Multinational Joint Task Force, which is based there.
At least 16 towns and villages in the area were razed.
Security analysts believe the targets of last weekend's attack were the civilian vigilantes helping the military in the counter-insurgency.
Hiding from view between the wall and the house, behind a roadside stall and the cover of a thick neem tree, Grema said the rampaging Islamists unleashed mayhem.
"All I could hear were ceaseless gunshots, explosions, screams from people and chants of 'Allahu Akbar' (God is greatest) from the Boko Haram gunmen," he added.
"I remained in my hiding place until Tuesday evening.
"Every night when it was dark, I would furtively scale the fence into my house to quickly eat garri (processed cassava granules) and drink water and go back to my hideout."
His family was not at home. They were in Kukawa, 40 kilometres (25 miles) away, paying their respects after Boko Haram killed his wife's cousin about two months ago.
"Some of the Boko Haram gunmen camped outside the Baga main market just 700 metres from my hideout," he explained.
"At night I could see lights from the power generator they ran. I could also hear their cheering and laughter.
"Luckily on Monday some of the gunmen withdrew while others stayed in the town. This reduced their number, which made it difficult for them to patrol the whole town. It worked to my advantage.
"On Tuesday they began looting the market and every home in the town… Around 6:00 pm (1700 GMT) they set fire to the market and began burning homes. I decided it was time I leave before they turn in my direction.
"Around 7:30 pm I ventured out of my hiding and started to walk away from the noise coming from the gunmen. It was dark, so no-one could see me."
– Nomad herdsman –
In the bush, Grema chanced upon an old man at a nomadic Fulani herdsmen's settlement, who advised him to move west to avoid running into the militants.
"His warning frightened me but made me more determined to get away. I thanked him and moved on," he said.
"I quickened my pace. I soon caught up with… four women. One of them was carrying a baby on her back.
"They told me they were among hundreds of women that were arrested by Boko Haram and detained in the home of the district head which Boko Haram had converted into a women's detention centre."
Three of the women had been separated from their children, he added.
Grema said he pushed out on his own, as the women were "too slow", running and walking throughout the night, before arriving at Kekeno village near Monguno, 65km away, the following morning.
On Thursday, he took a bus from Monguno to Maiduguri.
"I will never forget this experience and I will forever be grateful to the old Fulani nomad for his life-saving advice," he added.