When do impressions stop being funny and start being mean?

It all began with five minutes on NBC last Saturday night.

Titled The White Potus - a spin on hit HBO dark comedy The White Lotus - an SNL sketch depicted US president Donald Trump, his family and top team spending time at a fictional tropical hotel.

After jokes showing Eric Trump blending a gold Rolex watch and Ivanka Trump rejecting a spiritual call to give up material wealth, Wood's White Lotus character Chelsea is portrayed by cast member Sarah Sherman using a pronounced accent and large teeth.

In response to a comment made by a character playing US Health Secretary Robert F Kennedy Jr, she asks: "Fluoride? What's that?"

The mineral is added to some water supplies and brands of toothpaste to help prevent tooth decay.

For BBC Radio 4's Dead Ringers star Jan Ravens, the first misstep of the writers behind the SNL sketch was "not reading the room".

It was a bad idea to joke about someone's appearance in a sketch about The White Lotus, Ravens says, given Wood's casting has been praised for a character lacking "those all-American, fake-looking teeth".

"In the wake of all that, she's been talking about how she was bullied at school and the butt of jokes. So then you think, 'why would you do that joke'?"

It meant that in making fun of Wood's appearance, the sketch "punched down," says Ravens.

"You might make a joke about about Donald Trump's appearance because you're definitely not punching down on the most powerful man in the western world."

Ronni Ancona, co-writer and star of the early 2000s TV series The Big Impression, said she "could see" that the writers were also trying to make a point about US Health Secretary Robert F Kennedy Jr's pledge to remove fluoride from US drinking water.

But in doing so, "they would have made this tenuous link between fluoride and Aimee Lou's teeth. It's a bit of a cheap shot," she told BBC Breakfast on Tuesday.

After the show aired, Wood, 31, said she was "not thin skinned" and understood that SNL was about "caricature".

"But the whole joke was about fluoride," she wrote on Sunday. "I have big gap teeth not bad teeth."

Later on, in a post on social media, she said: "I've had apologies from SNL."

However, Francine Lewis, a comedian whose impersonations have earned her a large following on social media, says the whole purpose of the US show is to "take the mick".

While she can sympathise with someone being "embarrassed" by being the target of a sketch, Lewis adds that she thinks Wood's response was "too sensitive".

In her own impressions of celebrities, which include TV stars Gemma Collins and Stacey Solomon, Lewis has stuffed a pillow up her top to appear to be physically larger and put cotton wool on her teeth "to make them really white and jut out a bit".

In recent times, both fans and some of her targets have taken offence.

"I don't know if it's just the new generation of young people that just take offence to every little thing," she says.

"People that say you're a troll, you're a bully...I find myself hiding at celebrity events because I think 'oh I do their impression, they might not like me'."

But she believes that being impersonated is actually a marker of someone's popularity and fame, saying that "it means you've arrived".

Rather than adapting her impressions, Lewis is steadfast in her belief that "to make comedy funny, unfortunately you have to overstep the mark."

It's a view shared by Steve Nallon, known for impersonating former UK Prime Minister Margaret Thatcher on satirical TV programme Spitting Image.

"What caricaturists do by nature... is exaggerate the physicality. If a caricaturist is stopped from doing that, there's no point in him being a caricaturist," he says.

During the 1980s, one of his targets - former Labour minister Roy Hattersley - was mocked for a slight speech impediment, with water spurting out of his mouth as he spoke.

"The joke was Roy Hattesley spits," says Nallon, who adds that Hattesley allegedly got on board with the joke after initially taking offence.

For Nallon, those in the public eye will always be fair game. "Maybe it's not a bad lesson to learn that you've got to have the mickey taken out of you occasionally," he says.

But times have changed. Ravens says that "people are much more sensitive" about targeting certain aspects of people's appearances and mannerisms "than they used to be earlier on in my career, for example, and I think rightly so".

This is not the first time SNL has received criticism of their portrayals.

It doesn't mean the comedy is lost, says Ravens. In political satire - which was the main thrust of the SNL sketch - a really good impression satirises what the person is saying, rather than just fixating on how they look or how they deliver it, she adds.

During our phone interview, she seamlessly breaks into an impression of former UK Prime Minister Theresa May, but notes that just speaking in a tense, clipped way, "is only good for one line really".

"You're pricking pomposity and you're exposing hypocrisy. That's the point of satire."