Yes you are correct.
The transfer back is not a gift as it is their money.
No tax is due on the transfer of the capital but they may be liable to tax on any interest or dividends that is then generated.
If you qualify for split year then you only report any foreign income for the UK part of the year:
Residence, Domicile and Remittance Basis Manual
If you do not qualify then you will need to report all your foreign income to the UK:
Tax on foreign income
The guidance at RDRM12150 at www.gov.uk will help you work out if split year treatment applies.