〜たはいいが

Normally you cannot put particles straight after verbs, but in old Japanese this was acceptable and common. There are still remnants of this usage, and you’ll often see things like <verb>がよい which is a common (stiff) expression similar to <verb>たほうがいい (sounds very rough/imperative).

However, another common one is using past tense + はいい + が/けど, just like in this example sentence:

There is a good explanation on Japanese stack exchange about it.