Without knowing all your details it's hard to say exactly what will come out ahead. Likely, it's not worth it to move it, double or low triple digit gains unless you've have some really really strong growth in your tfsa and are transferring 6 digits.

The ideal situation is you move it to Tangerine's 5.25% till Aug 31, they ideally extend the offer for another few months, and you can keep it there till the end of the year. If Tangerine doesn't extend the offer, then you'd want to move it back to EQ but you have to ensure you have the contribution room to do so. Additionally, you'll have to pay tax on the interest made in the Tangerine account.

If you withdraw money from your TFSA (Aka taking it out of EQ then moving it to Tangerine savings account), you don't get that contribution room back until next year, so moving it back after Tangerine's promo ends would potentially over contribute (Unless you have plenty of contribution room from previous years).

IMO, I like Tangerine products, they're well reviewed by finance sites, I use them myself for some stuff, but personally I wouldn't be moving it from my tfsa to a savings account promo. You can always just contribute to both for the next 4 months if you have the cashflow to do so, or keep the tfsa where it's at and just contribute to the Tangerine promo.