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The white things are Hydras. Most likely came in on your plants. They are not a good thing to have as they can sting small/larval fish or invertebrates.
Fish like Guppies, Bettas or Gouramis tend to eat them but if you do not have any of these species, you can do physical removal with tweezers or chemical removal with medicines using fenbendazole ( make sure this med will not adversely effect anything in your tank prior to use. ) If there are no live fish or invertebrates in the tank or those can be removed temporarily to another tank, you can starve the hydra out but not adding any foods until the hydra have starved and died. This process will probably take a few weeks so it's not a quick fix but an effective one.