He picked up the bucket by the handle and walked off.
Tips
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The dī reading appears in only two compounds: 提防 (guard against, be vigilant) and 提溜 (carry by a handle, colloquial / northern). Everywhere else, 提 is read tí.
memory
Mnemonic: dī sounds clipped and wary - match it to 提防's alert, on-guard feel. The longer, lifted tí matches the open 'raise / bring up' sense.
Same hand radical as the tí reading. In 提溜 the hand sense is literal (gripping a handle); in 提防 the hand has bleached into a metaphor of 'holding up one's guard'.
Right 是 is the phonetic. The dī reading is a colloquial drift away from the main tí value, restricted to these two lexicalised compounds; the phonetic series (题, 堤) shows the same t/d alternation.
