I've tried it that way myself. I've tried it on wet paper towel as well. The problem with tubifex is the fact that it decays pretty quick after it dies, so you have to monitor it really good. I've had animals with flesh wounds due to bacterial infections on the throat, most likely due the tubifex. While eating, the animals their throats come in contact with the partially decaying tubifex. I wouldn't recommend feeding tubifex on land. It contains too much rubbish in between the knot of worms, even after rinsing it very well.
In the water the dead parts are eaten by snails and shrimp or the micro organisms in the water pretty quick. On land it takes way longer. At the same time the tubifex which is alive dies much faster on land. So rinsing it to the extreme will result in bad tubifex pretty soon after offering. I'm not saying that offering tubifex on land is bound to result in death and sorrow, but the risk is much higher compared to little worms and white worms.
If you're keeping them in a semi quatic setup (gravel heap in shallow water setup) than the risk is much smaller. Then I would suggest offering it on a piece of wet paper towel. The tubifex will crawl into the setup of course, but it will find water in order to survive. In a lid you've got the problem as you described and I haven't found a solution for it myself.