Understanding the factors associated with companion animal relinquishment is key in safeguarding animal welfare and human well-being. The aims of this study were to assess the effect of demographic variables on risk of relinquishment of cats and dogs during the COVID-19 pandemic, and to report characteristics of those that relinquished a cat or dog, and the experience of said relinquishment process. A series of surveys were administered to pet owners (n = 3,945) across several countries including the UK, USA, Canada, Italy, Spain and France. In total, n = 1,324 reported having acquired their cat or dog via online means. There was no association between online source (search engines, breeder websites, rescue websites, online ad sites and social media) and relinquishment status (NCR1 [Never Considered Relinquishment] compared to CR_R [Considering Relinquishment or already Relinquished]. More participants from the USA considered or already had relinquished their cat or dog compared to the UK and Italy. Of those that have already given up their pet, 76.2% agreed that it was an emotionally difficult decision, while 100% agreed that it was, logically, the correct decision. Demographic characteristics in those that reported considering relinquishment or that had already relinquished (CR_R; n = 146) were compared to a comparison group that had never considered relinquishing their pet (NCR2; n = 193). Being a male-gendered pet-owner and a younger pet age increased the risk of relinquishment. Cats and dogs from households with children were 4.6 times more likely to consider or have already relinquished a cat or dog compared to those from households without children. Further research is needed to explore risk of relinquishment of cats and dogs when children are present in the home.