Assuming that Party A only recognizes the bank's letter of guarantee, it is necessary to look at the requirements and restrictions on the bank according to the relevant provisions of the construction contract. If not, it is generally better to go to your own bank. If there is no limit in the bank, the bank will ask you to pay a high percentage of the deposit, even 100%. If the bank has a quota, the bank will provide you with a letter of guarantee under the quota, which will occupy part of the quota. If the line is a comprehensive credit line, it is not worth it. If you don't handle it in your own bank, you can choose to go outside to find a guarantee company, both good and bad. The advantage is that it doesn't occupy your own quota, the format of the letter of guarantee can be more flexible, and most of the deposit can be exempted (depending on qualifications and project conditions). The disadvantage is that the handling fee is relatively high, otherwise the guarantee company can't survive.
Assuming that Party A recognizes the letter of guarantee of the guarantee company, it will be simple. When you go to a guarantee company, you can generally avoid the deposit, and the handling fee is similar to that of going to a bank.
Anyway, the premise is that your company's credit card cannot have too many bad records, otherwise it will be difficult.