لم تعد القطة تخدش الباب.

In this sentence, لم تعد + imperfect verb means no longer or not anymore.

So لم تعد القطة تخدش الباب means that the cat used to scratch the door, but now it does not.

The basic imperfect form of عاد is تعود.

After لم, the verb must go into the jussive form. With a hollow verb like عاد, that changes تعود to تعدْ.

So:

• تعود = she returns / she goes back / she resumes
• لم تعد = she did not return / she no longer...

Before القطة, it is commonly pronounced تعدِ القطة because a helping vowel is inserted in speech.

لم is a negation particle that:

• negates an imperfect verb
• puts that verb into the jussive

Very often, لم + imperfect gives a past meaning like did not.

But with عاد + imperfect, the whole expression often has the idiomatic meaning no longer.

Because عاد is being used in a helper-like role here.

• تعد gives the idea of no longer
• تخدش gives the main action: scratch

So the structure is essentially:

لم تعد + verb = no longer + does that verb

In the imperfect, تـ can mark:

• you
• or she / it for a feminine singular subject

Here the subject is القطة, which is feminine singular, so both verbs are third-person feminine singular:

• تعد = she/it no longer...
• تخدش = she/it scratches

So here تـ does not mean you.

قطة is a feminine noun and specifically refers to a female cat.

That is why the verbs are feminine:

• تعد
• تخدش

If you used القط instead, you would normally use masculine verb forms:

لم يعد القط يخدش الباب

Yes.

By itself, عاد means returned or came back. So in another sentence:

لم تعد القطة إلى البيت
= The cat did not return home

But when لم تعد is followed directly by another imperfect verb, as in:

لم تعد القطة تخدش الباب

it is usually understood as no longer.

Because verb-first word order is very common in Arabic.

So لم تعد القطة تخدش الباب is a very normal Arabic sentence pattern.

You can also say:

القطة لم تعد تخدش الباب

That version is also correct, but it gives a bit more topic emphasis to the cat.

الباب is the direct object of تخدش.

The cat is doing the scratching, and the door is what is being scratched.

In fully vocalized Arabic, it would be accusative:

البابَ

In a fully vocalized version:

• القطةُ is nominative because it is the subject
• البابَ is accusative because it is the direct object

So the fully marked sentence is:

لَمْ تَعُدِ الْقِطَّةُ تَخْدِشُ الْبَابَ

In normal everyday writing, those case endings are usually not written.

The Arabic imperfect can express:

• a present action
• a repeated action
• a habitual action
• a general statement

In this sentence, the most natural meaning is habitual or general:

the cat no longer scratches the door
or
the cat doesn’t scratch the door anymore

A formal fully vocalized reading is:

لَمْ تَعُدِ الْقِطَّةُ تَخْدِشُ الْبَابَ

A rough pronunciation is:

lam taʿudi l-qiṭṭatu takhdishu l-bāba

In normal speech, many speakers reduce or drop full case endings, but this gives you the grammatical pronunciation.

Not if you want the standard MSA meaning no longer.

For this idea, Arabic commonly uses:

لم يعد + imperfect

So لم تعد القطة تخدش الباب is the natural MSA way to say the cat no longer scratches the door.

Using لا here would usually be understood differently, not as this standard not anymore expression.