The American squeezed into the uneven bars final thanks to an Olympic rule that limits only two finalists per nation, with two higher-placed Russians missing out.
Another Indian shooter Yashaswini Singh Deswal also failed to bag a medal, finishing 13th in the 10m air pistol event
Pranati got a quota place through reallocation since the Asian Championships, scheduled to be held in Tokyo in May, was cancelled due to COVID-19 pandemic.
Pranati will be the lone Indian gymnast to compete at the upcoming Tokyo Olympics.
Voss said the suits could also help to avoid embarrassment.
Becky's sister Ellie, who also competed at the 2016 Rio de Janeiro Games, has decided to take time out of the sport, however.
The world body in gymnastics will make an official announcement in this regard in June.
Geddert, who had ties to disgraced team doctor Larry Nassar, was charged earlier on Thursday with human trafficking and sexual assault.
Tinkler and others have spoken out about their experiences with British Gymnastics, accusing coaches of bullying and "body shaming".
USA Gymnastic tagged the wrong account rather than the four-time Olympic champion's verified account. Three hours later, Biles issued a tweet of her own.