*this is only my experience*
When I first started pods I just kept the used grounds in a sealed ziplock bag away from heat and light... This would start to smell and taste foul within hours.
If I did the same thing and kept it in the back of the refrigerator, they easily stayed 'fresh' (aka not foul tasting) for days.
What I recommend, if at all possible, is one of several options. One is to immediately do 2 washes and discard the grounds so do 2/3's your normal dose as the rewash (using my technique) was about 1/3 as potent as the first. Consume the 2 washes at once and there's no leftover and little love (aka alkaloids) lost.
Second you can consume the grounds whole (doing about 1/2 normal dose) in yogurt, chocolate milk, etc.
Third you could do half your dose as tea then immediately consume those spent pods in something like yogurt... This way you get the quicker-hitting tea and utilize the whole pod without having to worry about them becoming moldy. This is very efficient and healthier due to no worries of mold or bacteria from storing also when you consume grounds that have been washed, they are no where near as strong tasting and they have a softer texture than just consuming ground dry pod powder... I've never consumed fresh pods so keep this in mind.
Personally I just consumed whole grounds because it utilized the whole amount and was fastest but this comes on much slower. I was using them for pain so I was more concerned with efficiency than rush and many prefer the quicker onset tea provides.
For your original question- refrigerate/freeze, don't just leave spent grounds out for days whether in a jar, bag, whatever.
Lastly, if you consume part/all of your dose whole keep in mind that this elongates the effects some. This means if you are/become physically dependent that withdrawal will take longer to set in and last longer at slightly lower intensity.