Both are undergoing extensive re-sodding as crews work to repair the damage, which was clearly visible this week and last.
According to TMZ, the damage will cost in the region of $79,675 (£61,504) to fix.
The Rose Garden repairs come just weeks after the White House completed a major renovation of the garden intended, in part, to improve drainage issues.
White House spokesman Judd Deere said: “The sod is being replaced at no cost to taxpayers.
"Additionally, there has been other planned infrastructure work taking place on the south grounds".
He added that the work is expected to be completed by early Wednesday or Thursday, barring more bad weather. The president’s re-election campaign is said to be paying for the work.
The damage comes after Mr Trump upended long-held norms by using the White House grounds as the stage for a partisan political event.
The president formally accepted his party’s nomination on the South Lawn in front of more than a thousand people seated in rows of closely-packed white chairs, despite the ongoing pandemic.
He delivered his televised acceptance speech the final night of the convention in front of an audience of about 1,500 people, according to organisers. The event featured a large stage, giant screens and other equipment set on the South Lawn, in front of the majestic Washington Monument, and was capped by an elaborate fireworks show.
First lady Melania Trump delivered her convention speech in the newly-refurbished Rose Garden. The changes included the removal of crab apple trees, the addition of a 3-foot (0.91-metre)-wide limestone walking path, as well as what had been described as improvements to the garden’s drainage and broadcasting infrastructure. That work was paid with private donations and approved by the Committee for the Preservation of the White House.
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Officials noted that setup for the event began just after the renovation and after a span of heavy rain, and suggested that the new sod may therefore not have taken as well as it should have. The day of her speech, Astroturf was placed over the garden lawn because it was deemed a swampy mess.
Since the convention, the White House has avoided using the Rose Garden and South Lawn for public events. A Labor Day press conference was held in an unusual location — the White House’s North Portico — because of the construction. The president has been driving to the Joint Base Andrews for his trips out of town instead of taking the Marine One helicopter from the South Lawn because of the ongoing work.
His motorcade has also been loading and unloading along West Executive Avenue or the North Portico instead of the South Lawn driveway, which is currently blocked by equipment. Reporters covering White House events have been led through internal hallways instead of the West Wing colonnade to avoid being shown the mess.
The White House noted that some sod replacement is not unusual after major events, including the annual Easter Egg Roll and major state visits, especially if heavy foot traffic follows heavy rain. And since the sod is already being replaced, some other upgrades are being done as well.