5 official rulings from Bandai, last ruled Sep 13, 2024. Straight answers to how this card actually resolves.

When my opponent has a Digimon with 3000 DP or less, can I activate this card's effect and gain 1 memory but choose not to delete my opponent’s Digimon?
No. If there's a valid target, you must choose it when you activate the effect. You can't choose to not activate the effect when there is a valid target.
Ruled Sep 6, 2024
My opponent has a Digimon with 3000 DP or less and an effect that reads, “This Digimon can't be deleted by your opponent’s effects,” and another Digimon with 3000 DP or less but no effect. Can I intentionally have this card’s effect target the Digimon with the effect preventing deletion and gain 1 memory?
Yes. You can choose your opponent's Digimon with 3000 DP or less as a target, even if the chosen Digimon has an effect that prevents it from being deleted, in order to get the “if this effect didn't delete” part of the effect.
Ruled Sep 6, 2024
What does "while you have 0 or less memory" in this card’s inherited effect mean, exactly?
This inherited effect's condition is fulfilled if the memory is at 0 through 10 on your opponent's side when a DP-based deletion effect activates on a Digimon with this card in its digivolution cards.
Ruled Sep 6, 2024
What does an "add X000 to the maximum your DP-based deletion effects can delete" effect do?
Such effects increase the maximum value shown for DP-based deletion effects. For example, while "<Your Turn> Add 1000 to the maximum your DP-based deletion effects can delete" is activated, "<When Digivolving> Delete 1 of your opponent's Digimon with 3000 DP or less" will allow you to delete an opponent's Digimon with 4000 DP or less.
Ruled Sep 13, 2024
If "add X000 to the maximum your DP-based deletion effects can delete" is activating, can the maximum be increased for an effect such as "delete 1 of your opponent's Digimon with DP less than or equal to this Digimon's DP" that references a Digimon's DP for deletion?
No, it can't be increased. You can't increase the maximum of a DP-based deletion effect that doesn't show a numerical value.
Ruled Sep 13, 2024
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Questions and answers are Bandai's official rulings, collected and translated by the DigimonCardGame Wiki community and reused here under CC BY-SA. Card names and card text are © their respective publishers; Combalo is not affiliated with Bandai.