Hello Patience, a slight delay of reverse gear engagement could be an early warning sign of possible automatic transmission wear or damage. Whereas it may not always be a case of transmission damage it is worth investigating to rule out that possibility before the problem becomes a costly repair. There are a few factors that can cause automatic gearbox failure to engage reverse instantaneously. Low or ageing Automatic Transmission Fluid level (ATF) will reduce transmission hydraulic pressure, which will delay performance or engagement of the reverse gear or any other gears. A dirty and often clogged automatic transmission filter will prevent free flow of ATF. This will slow the hydraulic response of your gearbox.
A worn-out automatic transmission valve body or sticking valves will prevent quick buildup of ATF pressure. This will slow down the response of your gearbox when you engage reverse or forward gears. If the automatic gearbox clutch bands or clutch packs are worn out due to poor service, ageing or high mileage they are not likely to engage the reverse gear promptly. Electrical faults in your automatic transmission such as broken circuits, damaged wiring harness or bad solenoids and sensors can prevent prompt engagement of the reverse gear. If the reverse gear engages but is followed by a loud thud or thumping noise or even signs of gears slipping, then you need to quickly examine that gearbox for possible failure. Visit the nearest professional garage and have the gearbox checked.
My advice is to not ignore the delay in engagement of your reverse gear. Inspect the transmission fluid level and quality. Should you find the transmission fluid low, dirty or smelling burnt, then it should be serviced as soon as possible to prevent serious mechanical damage of your automatic gearbox. However, should there be signs of metallic debris in the sample of drained old oil, you should consider the likelihood of mechanical damage. You may need to repair or replace the faulty automatic gearbox.